]> Euler's Totient Function for n = 99001..100000

Euler's Totient Function for n = 99001..100000

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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	99001	99002	99003	99004	99005	99006	99007	99008	99009	99010
φ(n)	84852	48604	64800	48464	79200	31808	98280	36864	62208	39600

n	99011	99012	99013	99014	99015	99016	99017	99018	99019	99020
φ(n)	90000	31968	99012	47880	42240	49504	99016	33000	97744	39600

n	99021	99022	99023	99024	99025	99026	99027	99028	99029	99030
φ(n)	60912	38520	99022	32992	74240	48708	66012	46872	81144	26400

n	99031	99032	99033	99034	99035	99036	99037	99038	99039	99040
φ(n)	98272	49512	60000	45552	76384	28080	97920	47344	66024	39552

n	99041	99042	99043	99044	99045	99046	99047	99048	99049	99050
φ(n)	99040	31040	84888	45000	50400	49522	86400	33008	96336	33840

n	99051	99052	99053	99054	99055	99056	99057	99058	99059	99060
φ(n)	65280	49524	99052	33012	72000	48000	54912	49528	93216	24192

n	99061	99062	99063	99064	99065	99066	99067	99068	99069	99070
φ(n)	91872	49530	65988	40320	79248	28080	98280	49532	66044	39624

n	99071	99072	99073	99074	99075	99076	99077	99078	99079	99080
φ(n)	84912	32256	91440	49536	52800	44160	90060	28224	99078	39616

n	99081	99082	99083	99084	99085	99086	99087	99088	99089	99090
φ(n)	64800	48972	99082	31504	63936	44064	66056	44960	99088	26352

n	99091	99092	99093	99094	99095	99096	99097	99098	99099	99100
φ(n)	98392	42456	59136	49546	79272	33024	96640	49548	47520	39600

n	99101	99102	99103	99104	99105	99106	99107	99108	99109	99110
φ(n)	98112	32472	99102	46656	52848	42468	91080	33024	99108	33280

n	99111	99112	99113	99114	99115	99116	99117	99118	99119	99120
φ(n)	66072	45696	84948	33036	77280	48720	66060	49558	99118	22272

n	99121	99122	99123	99124	99125	99126	99127	99128	99129	99130
φ(n)	90100	47824	59616	49560	72000	33036	79968	49560	65360	37840

n	99131	99132	99133	99134	99135	99136	99137	99138	99139	99140
φ(n)	99130	30000	99132	41472	52848	49536	99136	28800	99138	39648

n	99141	99142	99143	99144	99145	99146	99147	99148	99149	99150
φ(n)	56640	46944	90120	31104	78000	48928	66096	42480	99148	26400

n	99151	99152	99153	99154	99155	99156	99157	99158	99159	99160
φ(n)	88032	49568	63096	45060	67968	33048	98496	48384	66104	38016

n	99161	99162	99163	99164	99165	99166	99167	99168	99169	99170
φ(n)	88128	28296	97240	45744	48000	49128	98280	33024	82080	38640

n	99171	99172	99173	99174	99175	99176	99177	99178	99179	99180
φ(n)	66096	49584	99172	33056	79320	36960	61008	46656	95120	24192

n	99181	99182	99183	99184	99185	99186	99187	99188	99189	99190
φ(n)	99180	49000	56664	49584	78064	32400	88200	48960	64872	31104

n	99191	99192	99193	99194	99195	99196	99197	99198	99199	99200
φ(n)	99190	33056	98560	49596	49664	49596	82512	29880	89496	38400

n	99201	99202	99203	99204	99205	99206	99207	99208	99209	99210
φ(n)	64512	49152	91416	28320	79360	49602	64800	49600	86800	26448

n	99211	99212	99213	99214	99215	99216	99217	99218	99219	99220
φ(n)	85032	46656	66140	49056	79368	29952	97060	40176	66144	35200

n	99221	99222	99223	99224	99225	99226	99227	99228	99229	99230
φ(n)	98592	31592	99222	48672	45360	49612	97680	33072	86016	39688

n	99231	99232	99233	99234	99235	99236	99237	99238	99239	99240
φ(n)	57600	42432	99232	31968	78144	49616	62640	47096	85056	26432

n	99241	99242	99243	99244	99245	99246	99247	99248	99249	99250
φ(n)	99240	41520	66156	48384	75856	26496	97560	49616	66164	39600

n	99251	99252	99253	99254	99255	99256	99257	99258	99259	99260
φ(n)	99250	33048	77280	49626	48768	46944	99256	32480	99258	33984

n	99261	99262	99263	99264	99265	99266	99267	99268	99269	99270
φ(n)	64320	48000	93408	29440	79408	49632	54432	43296	97344	26448

n	99271	99272	99273	99274	99275	99276	99277	99278	99279	99280
φ(n)	96552	49632	66180	42504	68400	33088	99276	49638	66168	36864

n	99281	99282	99283	99284	99285	99286	99287	99288	99289	99290
φ(n)	78480	33092	98200	49640	52944	45120	96936	28224	99288	39712

n	99291	99292	99293	99294	99295	99296	99297	99298	99299	99300
φ(n)	63272	48960	96060	28512	68064	47488	55680	49140	98280	26400

n	99301	99302	99303	99304	99305	99306	99307	99308	99309	99310
φ(n)	98604	41280	65208	49648	79440	33048	91656	43200	56736	39720

n	99311	99312	99313	99314	99315	99316	99317	99318	99319	99320
φ(n)	97152	33088	94068	44352	52944	42552	99316	33104	90280	36480

n	99321	99322	99323	99324	99325	99326	99327	99328	99329	99330
φ(n)	66212	48672	85092	31680	76160	49662	65408	49152	97860	20160

n	99331	99332	99333	99334	99335	99336	99337	99338	99339	99340
φ(n)	93472	47016	60912	49666	79464	33104	81312	49668	66224	39728

n	99341	99342	99343	99344	99345	99346	99347	99348	99349	99350
φ(n)	90200	33108	96880	42528	51264	45840	99346	31104	99348	39720

n	99351	99352	99353	99354	99355	99356	99357	99358	99359	99360
φ(n)	53136	45120	97920	31920	76800	48720	66236	41400	91704	25344

n	99361	99362	99363	99364	99365	99366	99367	99368	99369	99370
φ(n)	97812	49680	60200	49680	63744	33120	99366	49680	64800	37584

n	99371	99372	99373	99374	99375	99376	99377	99378	99379	99380
φ(n)	99370	26208	97020	45160	52000	49680	99376	33120	85176	39744

n	99381	99382	99383	99384	99385	99386	99387	99388	99389	99390
φ(n)	65520	44928	91168	32000	66240	41040	66096	49692	94140	26496

n	99391	99392	99393	99394	99395	99396	99397	99398	99399	99400
φ(n)	99390	49664	56784	49696	78336	30000	99396	45864	62336	33600

n	99401	99402	99403	99404	99405	99406	99407	99408	99409	99410
φ(n)	99400	33132	98368	49700	51888	47520	77400	31104	99408	39760

n	99411	99412	99413	99414	99415	99416	99417	99418	99419	99420
φ(n)	61152	47936	98208	28296	77952	45696	64080	45180	96696	26496

n	99421	99422	99423	99424	99425	99426	99427	99428	99429	99430
φ(n)	85176	49710	66276	45696	76800	32544	94176	41184	57200	38880

n	99431	99432	99433	99434	99435	99436	99437	99438	99439	99440
φ(n)	99430	33120	93568	49036	45408	49716	91776	33144	99438	35840

n	99441	99442	99443	99444	99445	99446	99447	99448	99449	99450
φ(n)	63504	42612	98808	33144	79552	47088	66296	48000	85236	23040

n	99451	99452	99453	99454	99455	99456	99457	99458	99459	99460
φ(n)	90400	46552	66300	49726	79560	27648	98820	49506	64512	39776

n	99461	99462	99463	99464	99465	99466	99467	99468	99469	99470
φ(n)	98124	29920	78624	49728	50112	48480	93600	33048	99468	32928

n	99471	99472	99473	99474	99475	99476	99477	99478	99479	99480
φ(n)	65240	49728	90420	32480	75680	45888	56808	49738	96240	26496

n	99481	99482	99483	99484	99485	99486	99487	99488	99489	99490
φ(n)	97552	49740	66320	34560	78400	33156	99486	49728	61200	39792

n	99491	99492	99493	99494	99495	99496	99497	99498	99499	99500
φ(n)	83520	33160	96768	49746	47520	49744	99496	26928	92736	39600

n	99501	99502	99503	99504	99505	99506	99507	99508	99509	99510
φ(n)	62400	44352	94248	33120	68208	45220	64640	49752	98700	25440

n	99511	99512	99513	99514	99515	99516	99517	99518	99519	99520
φ(n)	98800	42624	66336	49756	73440	33168	88560	46816	56784	39680

n	99521	99522	99523	99524	99525	99526	99527	99528	99529	99530
φ(n)	95172	31104	99522	49128	53040	42648	99526	26880	99528	38592

n	99531	99532	99533	99534	99535	99536	99537	99538	99539	99540
φ(n)	66348	49136	83520	32448	74880	49760	66356	49296	90480	22464

n	99541	99542	99543	99544	99545	99546	99547	99548	99549	99550
φ(n)	84240	49000	66360	47520	77616	32384	85320	48480	66312	36000

n	99551	99552	99553	99554	99555	99556	99557	99558	99559	99560
φ(n)	99550	30720	98560	39312	53088	49776	96096	33180	99558	37440

n	99561	99562	99563	99564	99565	99566	99567	99568	99569	99570
φ(n)	51600	48972	99562	33184	79648	49782	57024	42336	93696	26544

n	99571	99572	99573	99574	99575	99576	99577	99578	99579	99580
φ(n)	99570	43200	66380	49786	68160	33120	99576	49788	62856	36672

n	99581	99582	99583	99584	99585	99586	99587	99588	99589	99590
φ(n)	99580	28440	90420	49664	53088	44800	97656	32256	83040	38016

n	99591	99592	99593	99594	99595	99596	99597	99598	99599	99600
φ(n)	65472	48720	89424	30120	79672	42672	66396	47160	98736	26240

n	99601	99602	99603	99604	99605	99606	99607	99608	99609	99610
φ(n)	98532	49800	51840	48384	72400	30624	99606	49800	66404	34128

n	99611	99612	99613	99614	99615	99616	99617	99618	99619	99620
φ(n)	99610	33192	92400	49806	51072	45120	80136	33204	89856	37376

n	99621	99622	99623	99624	99625	99626	99627	99628	99629	99630
φ(n)	66408	49810	99622	28416	79600	49248	60360	49812	98076	25920

n	99631	99632	99633	99634	99635	99636	99637	99638	99639	99640
φ(n)	83160	45888	66420	48180	79704	30096	93760	38760	66420	38272

n	99641	99642	99643	99644	99645	99646	99647	99648	99649	99650
φ(n)	96912	33212	99642	48048	41472	49822	99000	33024	90580	39840

n	99651	99652	99653	99654	99655	99656	99657	99658	99659	99660
φ(n)	65192	42696	98988	31232	75456	49824	66420	45984	81576	24000

n	99661	99662	99663	99664	99665	99666	99667	99668	99669	99670
φ(n)	99660	49830	65688	49824	77040	28224	99666	49832	66444	39864

n	99671	99672	99673	99674	99675	99676	99677	99678	99679	99680
φ(n)	76800	33216	82320	45360	53040	49836	99036	32256	99678	33792

n	99681	99682	99683	99684	99685	99686	99687	99688	99689	99690
φ(n)	65712	43120	98400	30240	79744	49842	55200	46848	99688	26576

n	99691	99692	99693	99694	99695	99696	99697	99698	99699	99700
φ(n)	98800	49844	56160	42720	78624	31680	92016	49140	65736	39840

n	99701	99702	99703	99704	99705	99706	99707	99708	99709	99710
φ(n)	85452	31920	98968	44880	47872	49852	99706	28464	99708	36192

n	99711	99712	99713	99714	99715	99716	99717	99718	99719	99720
φ(n)	66420	46080	99712	33236	60480	49152	64848	49104	99718	26496

n	99721	99722	99723	99724	99725	99726	99727	99728	99729	99730
φ(n)	99720	40128	61344	49184	79760	30200	96480	47520	56952	39888

n	99731	99732	99733	99734	99735	99736	99737	99738	99739	99740
φ(n)	90720	33240	99732	48760	51840	39168	90660	33228	93856	39888

n	99741	99742	99743	99744	99745	99746	99747	99748	99749	99750
φ(n)	66492	49870	85488	33216	79792	48880	66492	45320	92064	21600

n	99751	99752	99753	99754	99755	99756	99757	99758	99759	99760
φ(n)	95392	48384	64800	49876	78400	31104	85500	48240	60440	37632

n	99761	99762	99763	99764	99765	99766	99767	99768	99769	99770
φ(n)	99760	30672	98208	42672	53136	49200	99766	33248	91872	36240

n	99771	99772	99773	99774	99775	99776	99777	99778	99779	99780
φ(n)	57000	49884	93888	31680	73440	49856	65520	42756	98784	26592

n	99781	99782	99783	99784	99785	99786	99787	99788	99789	99790
φ(n)	88320	49890	66516	49888	68400	33260	99786	43200	60480	37504

n	99791	99792	99793	99794	99795	99796	99797	99798	99799	99800
φ(n)	98352	25920	99792	48640	53216	48960	95436	33264	83616	39840

n	99801	99802	99803	99804	99805	99806	99807	99808	99809	99810
φ(n)	61344	49404	88200	33264	79840	42768	58752	49888	99808	26592

n	99811	99812	99813	99814	99815	99816	99817	99818	99819	99820
φ(n)	99000	49904	56448	41760	79848	33264	99816	48160	66528	31680

n	99821	99822	99823	99824	99825	99826	99827	99828	99829	99830
φ(n)	99072	32760	99822	46848	48400	45360	78912	32016	99828	39072

n	99831	99832	99833	99834	99835	99836	99837	99838	99839	99840
φ(n)	65720	49912	99832	28512	77760	45360	66552	49918	99838	24576

n	99841	99842	99843	99844	99845	99846	99847	99848	99849	99850
φ(n)	80448	49920	63624	49248	75600	32508	87360	42768	65600	39920

n	99851	99852	99853	99854	99855	99856	99857	99858	99859	99860
φ(n)	96600	32448	92160	49926	45504	49296	98160	28160	99858	39936

n	99861	99862	99863	99864	99865	99866	99867	99868	99869	99870
φ(n)	66572	42756	97128	31104	79888	43824	66576	49932	77760	26624

n	99871	99872	99873	99874	99875	99876	99877	99878	99879	99880
φ(n)	99870	49920	66096	49936	73600	26880	99876	49938	61152	36160

n	99881	99882	99883	99884	99885	99886	99887	99888	99889	99890
φ(n)	99880	32040	81000	49940	53264	49942	98136	33280	92400	34224

n	99891	99892	99893	99894	99895	99896	99897	99898	99899	99900
φ(n)	60480	43008	99180	33296	79912	49944	55440	49500	99264	25920

n	99901	99902	99903	99904	99905	99906	99907	99908	99909	99910
φ(n)	99900	42840	66600	42624	69888	33300	99906	49952	62592	39168

n	99911	99912	99913	99914	99915	99916	99917	99918	99919	99920
φ(n)	85596	31680	87600	49956	53280	49956	97440	25920	99144	39936

n	99921	99922	99923	99924	99925	99926	99927	99928	99929	99930
φ(n)	63072	48852	99922	30240	68400	47008	66600	49960	99928	26640

n	99931	99932	99933	99934	99935	99936	99937	99938	99939	99940
φ(n)	92232	41328	66620	48216	68640	33216	95904	49396	57096	37728

n	99941	99942	99943	99944	99945	99946	99947	99948	99949	99950
φ(n)	99084	33312	94048	44640	53280	38280	98736	33312	99036	39960

n	99951	99952	99953	99954	99955	99956	99957	99958	99959	99960
φ(n)	66632	49968	84240	33264	79960	49976	55680	45760	94680	21504

n	99961	99962	99963	99964	99965	99966	99967	99968	99969	99970
φ(n)	99960	49500	64176	49104	79968	33320	85680	44800	65136	36864

n	99971	99972	99973	99974	99975	99976	99977	99978	99979	99980
φ(n)	99970	33312	99328	41472	50400	49984	94080	31536	88800	39984

n	99981	99982	99983	99984	99985	99986	99987	99988	99989	99990
φ(n)	54648	49990	92280	33312	79984	49992	66656	42840	99988	24000

n	99991	99992	99993	99994	99995	99996	99997	99998	99999	100000
φ(n)	99990	48160	66660	46784	68544	30720	94392	49998	64800	40000

J.P. Martin-Flatin