﻿ ]> Euler's Totient Function for n = 98001..99000

Euler's Totient Function for n = 98001..99000

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Euler's totient function (also known as the "phi function") counts the number of natural integers less than n that are coprime to n. It is very useful in number theory, e.g. to compute the number of primitive roots modulo a prime n. For more information, see:

• Wikipedia
• Encyclopedia of Mathematics
• Lindsay N. Childs, A Concrete Introduction to Higher Algebra, 3rd ed., Springer, 2009, pp. 111 and 179-180.
• G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, 6th ed., Oxford University Press, 2008, pp. 63-65.

The values presented below were computed in 2015 using a Python program.

 n 98001 98002 98003 98004 98005 98006 98007 98008 98009 98010 φ(n) 65328 46404 93720 32664 73728 49002 51552 49000 98008 23760
 n 98011 98012 98013 98014 98015 98016 98017 98018 98019 98020 φ(n) 98010 48336 63504 42000 78408 32640 98016 49008 65340 34944
 n 98021 98022 98023 98024 98025 98026 98027 98028 98029 98030 φ(n) 71280 29760 96760 49008 52240 46860 96360 27936 97276 39208
 n 98031 98032 98033 98034 98035 98036 98037 98038 98039 98040 φ(n) 63680 44480 90480 32676 67200 49016 65340 49018 89856 24192
 n 98041 98042 98043 98044 98045 98046 98047 98048 98049 98050 φ(n) 98040 40848 59400 48384 78432 30096 98046 48896 51744 37440
 n 98051 98052 98053 98054 98055 98056 98057 98058 98059 98060 φ(n) 96600 32680 94860 44560 52272 39168 98056 32016 85536 39216
 n 98061 98062 98063 98064 98065 98066 98067 98068 98069 98070 φ(n) 65372 49030 84048 32544 71280 49032 64512 49032 97440 22368
 n 98071 98072 98073 98074 98075 98076 98077 98078 98079 98080 φ(n) 97000 42240 61440 49036 78440 29680 84060 44352 65384 39168
 n 98081 98082 98083 98084 98085 98086 98087 98088 98089 98090 φ(n) 98080 32688 95760 40320 48192 49042 86400 31680 95956 36864
 n 98091 98092 98093 98094 98095 98096 98097 98098 98099 98100 φ(n) 55728 48416 97440 32696 74976 49040 61920 35280 97464 25920
 n 98101 98102 98103 98104 98105 98106 98107 98108 98109 98110 φ(n) 98100 48600 64064 49048 67248 32144 88704 49052 59400 39240
 n 98111 98112 98113 98114 98115 98116 98117 98118 98119 98120 φ(n) 90552 27648 95680 49056 50400 46440 96396 30888 82680 35520
 n 98121 98122 98123 98124 98125 98126 98127 98128 98129 98130 φ(n) 65412 48300 98122 27648 78000 40824 65412 49056 98128 26160
 n 98131 98132 98133 98134 98135 98136 98137 98138 98139 98140 φ(n) 89100 49064 56064 48576 74304 30912 90576 49068 65424 33600
 n 98141 98142 98143 98144 98145 98146 98147 98148 98149 98150 φ(n) 88000 29720 98142 49056 52272 47460 84084 32712 96480 36000
 n 98151 98152 98153 98154 98155 98156 98157 98158 98159 98160 φ(n) 65432 49072 89220 25920 77088 48048 65436 46176 97104 26112
 n 98161 98162 98163 98164 98165 98166 98167 98168 98169 98170 φ(n) 81648 49080 60336 42240 75712 32720 96976 42048 63840 39264
 n 98171 98172 98173 98174 98175 98176 98177 98178 98179 98180 φ(n) 97272 32400 92988 48640 38400 44544 94980 32724 98178 39264
 n 98181 98182 98183 98184 98185 98186 98187 98188 98189 98190 φ(n) 65448 42072 96048 32720 77184 44620 62568 49092 76752 26160
 n 98191 98192 98193 98194 98195 98196 98197 98198 98199 98200 φ(n) 97384 43776 64400 47376 76480 27888 87360 47736 65448 39200
 n 98201 98202 98203 98204 98205 98206 98207 98208 98209 98210 φ(n) 97572 30192 84168 49100 52368 49102 98206 28800 89856 31680
 n 98211 98212 98213 98214 98215 98216 98217 98218 98219 98220 φ(n) 61992 47880 98212 32736 72480 49104 56088 49108 89280 26176
 n 98221 98222 98223 98224 98225 98226 98227 98228 98229 98230 φ(n) 98220 48312 63168 42048 78560 30528 98226 45312 64736 33120
 n 98231 98232 98233 98234 98235 98236 98237 98238 98239 98240 φ(n) 84192 32736 93940 49116 50112 47840 97536 28056 95040 39168
 n 98241 98242 98243 98244 98245 98246 98247 98248 98249 98250 φ(n) 54720 49120 92448 32736 67200 49122 65496 49120 93060 26000
 n 98251 98252 98253 98254 98255 98256 98257 98258 98259 98260 φ(n) 98250 36960 65448 45336 76608 30976 98256 48384 56136 36992
 n 98261 98262 98263 98264 98265 98266 98267 98268 98269 98270 φ(n) 97152 31824 89320 48160 52400 42108 90696 30960 98268 37920
 n 98271 98272 98273 98274 98275 98276 98277 98278 98279 98280 φ(n) 64080 47232 82800 29760 78600 48360 58880 49138 93984 20736
 n 98281 98282 98283 98284 98285 98286 98287 98288 98289 98290 φ(n) 94864 48672 65160 49140 71440 32760 79704 49136 64152 39312
 n 98291 98292 98293 98294 98295 98296 98297 98298 98299 98300 φ(n) 97632 32760 90720 38976 52416 44640 98296 31752 98298 39280
 n 98301 98302 98303 98304 98305 98306 98307 98308 98309 98310 φ(n) 54000 46992 97608 32768 78640 42768 59400 42120 95616 25088
 n 98311 98312 98313 98314 98315 98316 98317 98318 98319 98320 φ(n) 92512 49152 65540 49156 66144 32760 98316 43200 60480 39296
 n 98321 98322 98323 98324 98325 98326 98327 98328 98329 98330 φ(n) 98320 28080 98322 48024 47520 48720 98326 30720 76560 39328
 n 98331 98332 98333 98334 98335 98336 98337 98338 98339 98340 φ(n) 64512 43200 97308 32724 77280 42048 65556 49168 94920 23680
 n 98341 98342 98343 98344 98345 98346 98347 98348 98349 98350 φ(n) 96012 49170 55944 46512 67584 31824 98346 46992 65564 33600
 n 98351 98352 98353 98354 98355 98356 98357 98358 98359 98360 φ(n) 89400 32736 96628 49176 51168 48312 84300 29952 95920 39328
 n 98361 98362 98363 98364 98365 98366 98367 98368 98369 98370 φ(n) 65556 41920 89640 28080 77520 48688 65576 46592 98368 26208
 n 98371 98372 98373 98374 98375 98376 98377 98378 98379 98380 φ(n) 72864 49184 59400 48600 78600 32784 98376 42156 61632 39344
 n 98381 98382 98383 98384 98385 98386 98387 98388 98389 98390 φ(n) 97500 31032 95688 40320 44928 49192 98386 32760 98388 39352
 n 98391 98392 98393 98394 98395 98396 98397 98398 98399 98400 φ(n) 65592 42000 96720 30360 71520 46272 58464 49198 84336 25600
 n 98401 98402 98403 98404 98405 98406 98407 98408 98409 98410 φ(n) 93204 49200 65600 48384 78720 25200 98406 49200 65604 36288
 n 98411 98412 98413 98414 98415 98416 98417 98418 98419 98420 φ(n) 98410 32016 79296 49206 52488 49200 85360 32016 98418 31104
 n 98421 98422 98423 98424 98425 98426 98427 98428 98429 98430 φ(n) 64272 49210 88704 32784 75600 47488 54432 44720 98428 24576
 n 98431 98432 98433 98434 98435 98436 98437 98438 98439 98440 φ(n) 97792 49152 65616 41184 78744 30240 97696 48544 56160 37312
 n 98441 98442 98443 98444 98445 98446 98447 98448 98449 98450 φ(n) 82320 32796 98442 49220 52496 49222 92640 28032 90864 35600
 n 98451 98452 98453 98454 98455 98456 98457 98458 98459 98460 φ(n) 65628 48600 98452 32160 64512 47520 63792 46620 98458 26208
 n 98461 98462 98463 98464 98465 98466 98467 98468 98469 98470 φ(n) 89500 38880 62744 46080 76912 32820 98466 48552 56160 38304
 n 98471 98472 98473 98474 98475 98476 98477 98478 98479 98480 φ(n) 96744 29760 98472 48256 48000 42192 90720 32820 98478 39360
 n 98481 98482 98483 98484 98485 98486 98487 98488 98489 98490 φ(n) 61760 48000 76680 31584 78784 47080 63360 45408 97680 22176
 n 98491 98492 98493 98494 98495 98496 98497 98498 98499 98500 φ(n) 98490 49244 65660 43560 78792 31104 84420 46336 65664 39200
 n 98501 98502 98503 98504 98505 98506 98507 98508 98509 98510 φ(n) 90912 32832 97648 42192 47520 49252 98506 32832 94204 39400
 n 98511 98512 98513 98514 98515 98516 98517 98518 98519 98520 φ(n) 56280 47840 91728 30240 69120 44760 65676 40680 98518 26240
 n 98521 98522 98523 98524 98525 98526 98527 98528 98529 98530 φ(n) 97252 49260 63360 49260 67440 32840 81120 49248 65684 38512
 n 98531 98532 98533 98534 98535 98536 98537 98538 98539 98540 φ(n) 95832 25344 98532 46656 52544 48384 97860 29840 84420 36288
 n 98541 98542 98543 98544 98545 98546 98547 98548 98549 98550 φ(n) 65688 47544 98542 32832 78832 42228 64872 48440 81600 25920
 n 98551 98552 98553 98554 98555 98556 98557 98558 98559 98560 φ(n) 97704 48384 49248 49276 75328 31920 97020 49278 64032 30720
 n 98561 98562 98563 98564 98565 98566 98567 98568 98569 98570 φ(n) 98560 32852 98562 48000 52560 42624 84480 31968 97920 39424
 n 98571 98572 98573 98574 98575 98576 98577 98578 98579 98580 φ(n) 57120 46656 98572 28152 78840 48000 65664 47124 90984 24960
 n 98581 98582 98583 98584 98585 98586 98587 98588 98589 98590 φ(n) 84492 44800 61824 49288 78864 32856 97960 42168 64496 39432
 n 98591 98592 98593 98594 98595 98596 98597 98598 98599 98600 φ(n) 93384 29952 89620 49296 44928 48984 98596 32864 96264 35840
 n 98601 98602 98603 98604 98605 98606 98607 98608 98609 98610 φ(n) 62832 42252 97800 29520 69120 48208 65736 49296 84516 24768
 n 98611 98612 98613 98614 98615 98616 98617 98618 98619 98620 φ(n) 95400 48576 65736 49306 71280 28128 92800 45504 64680 39440
 n 98621 98622 98623 98624 98625 98626 98627 98628 98629 98630 φ(n) 98620 32868 82944 46464 52400 44820 98626 32872 89712 33792
 n 98631 98632 98633 98634 98635 98636 98637 98638 98639 98640 φ(n) 60480 49312 96720 30912 78904 49316 50400 48840 98638 26112
 n 98641 98642 98643 98644 98645 98646 98647 98648 98649 98650 φ(n) 98640 45360 65000 38880 77760 32000 94336 41760 64512 39440
 n 98651 98652 98653 98654 98655 98656 98657 98658 98659 98660 φ(n) 79488 32880 96508 48760 52608 49312 91056 27216 89680 39456
 n 98661 98662 98663 98664 98665 98666 98667 98668 98669 98670 φ(n) 65772 49330 98662 32880 67632 49332 62208 46400 98668 21120
 n 98671 98672 98673 98674 98675 98676 98677 98678 98679 98680 φ(n) 97344 42240 63600 48756 78920 32880 97600 49338 54432 39456
 n 98681 98682 98683 98684 98685 98686 98687 98688 98689 98690 φ(n) 89700 32892 91080 49340 48384 39312 91840 32768 98688 38640
 n 98691 98692 98693 98694 98695 98696 98697 98698 98699 98700 φ(n) 64680 44840 80784 32892 78952 44928 65072 48480 98040 22080
 n 98701 98702 98703 98704 98705 98706 98707 98708 98709 98710 φ(n) 97504 46432 59760 47520 74736 32900 82824 49352 60720 39480
 n 98711 98712 98713 98714 98715 98716 98717 98718 98719 98720 φ(n) 98710 32832 98712 38400 52640 44352 98716 32904 92896 39424
 n 98721 98722 98723 98724 98725 98726 98727 98728 98729 98730 φ(n) 56376 45552 98088 31104 71600 49362 65816 40320 98728 26304
 n 98731 98732 98733 98734 98735 98736 98737 98738 98739 98740 φ(n) 98730 49364 65820 49366 60480 28160 98736 49368 61776 39488
 n 98741 98742 98743 98744 98745 98746 98747 98748 98749 98750 φ(n) 98112 28200 93528 49368 50624 48768 87400 30240 84636 39000
 n 98751 98752 98753 98754 98755 98756 98757 98758 98759 98760 φ(n) 65832 49344 89856 32400 79000 42312 65832 44220 97080 26304
 n 98761 98762 98763 98764 98765 98766 98767 98768 98769 98770 φ(n) 89040 44352 56424 49380 79008 31320 98136 49376 57600 31488
 n 98771 98772 98773 98774 98775 98776 98777 98778 98779 98780 φ(n) 96432 32920 98772 43680 52560 49384 83232 32400 98778 35840
 n 98781 98782 98783 98784 98785 98786 98787 98788 98789 98790 φ(n) 62352 49390 98040 28224 75504 49392 56832 49392 98124 25344
 n 98791 98792 98793 98794 98795 98796 98797 98798 98799 98800 φ(n) 76920 48256 65844 48300 79032 32928 95580 42336 65864 34560
 n 98801 98802 98803 98804 98805 98806 98807 98808 98809 98810 φ(n) 98800 29880 95368 46464 45120 48888 98806 31328 98808 38400
 n 98811 98812 98813 98814 98815 98816 98817 98818 98819 98820 φ(n) 65868 42336 82800 32088 79048 49152 65876 49408 80136 25920
 n 98821 98822 98823 98824 98825 98826 98827 98828 98829 98830 φ(n) 92992 49410 65880 44880 76560 25920 96120 47760 64584 39528
 n 98831 98832 98833 98834 98835 98836 98837 98838 98839 98840 φ(n) 94512 31360 84672 49416 47840 49416 98836 29376 91224 33792
 n 98841 98842 98843 98844 98845 98846 98847 98848 98849 98850 φ(n) 64400 48672 97728 32944 77376 44920 56376 49408 98848 26320
 n 98851 98852 98853 98854 98855 98856 98857 98858 98859 98860 φ(n) 96400 45600 64944 40392 74368 32928 83160 49428 63720 39536
 n 98861 98862 98863 98864 98865 98866 98867 98868 98869 98870 φ(n) 81648 32952 97848 47808 48672 49432 98866 25440 98868 39544
 n 98871 98872 98873 98874 98875 98876 98877 98878 98879 98880 φ(n) 65912 46464 98872 32940 67200 46800 63008 45624 88000 26112
 n 98881 98882 98883 98884 98885 98886 98887 98888 98889 98890 φ(n) 97200 42336 65916 48488 79104 32960 98886 48208 52992 33600
 n 98891 98892 98893 98894 98895 98896 98897 98898 98899 98900 φ(n) 91272 31680 98892 49000 49824 42336 98896 32240 98898 36960
 n 98901 98902 98903 98904 98905 98906 98907 98908 98909 98910 φ(n) 58320 49450 83160 30336 78000 46528 65936 48672 98908 22464
 n 98911 98912 98913 98914 98915 98916 98917 98918 98919 98920 φ(n) 98910 44800 65940 46512 77760 32968 78192 49458 63504 39552
 n 98921 98922 98923 98924 98925 98926 98927 98928 98929 98930 φ(n) 95700 32972 80960 42384 52720 49462 98926 32832 98928 36480
 n 98931 98932 98933 98934 98935 98936 98937 98938 98939 98940 φ(n) 56448 49464 90720 29960 77280 48544 65952 41040 98938 24576
 n 98941 98942 98943 98944 98945 98946 98947 98948 98949 98950 φ(n) 98172 48600 58464 49408 61440 31416 98946 47712 65964 39560
 n 98951 98952 98953 98954 98955 98956 98957 98958 98959 98960 φ(n) 97032 25920 98952 49476 52704 41280 93120 32984 83160 39552
 n 98961 98962 98963 98964 98965 98966 98967 98968 98969 98970 φ(n) 65972 49480 98962 32976 79168 42408 59960 48576 87120 26384
 n 98971 98972 98973 98974 98975 98976 98977 98978 98979 98980 φ(n) 93744 48816 56520 44800 76320 32960 95536 44880 65984 33600
 n 98981 98982 98983 98984 98985 98986 98987 98988 98989 98990 φ(n) 98980 29808 94860 49488 52784 48300 83304 32256 89980 37440
 n 98991 98992 98993 98994 98995 98996 98997 98998 98999 99000 φ(n) 62016 47168 98992 28272 73056 49496 65996 49498 98998 24000

J.P. Martin-Flatin