]> Euler's Totient Function for n = 40001..41000

Euler's Totient Function for n = 40001..41000

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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	40001	40002	40003	40004	40005	40006	40007	40008	40009	40010
φ(n)	34560	12992	39528	19584	18144	19680	36360	13328	40008	16000

n	40011	40012	40013	40014	40015	40016	40017	40018	40019	40020
φ(n)	26672	17136	40012	11664	31200	19200	26676	16960	34296	9856

n	40021	40022	40023	40024	40025	40026	40027	40028	40029	40030
φ(n)	38700	20010	26676	20008	32000	11424	36936	20012	24240	16008

n	40031	40032	40033	40034	40035	40036	40037	40038	40039	40040
φ(n)	40030	13248	31752	19440	19968	20016	40036	13344	40038	11520

n	40041	40042	40043	40044	40045	40046	40047	40048	40049	40050
φ(n)	26676	20020	38280	12880	32032	20022	22872	20016	38640	10560

n	40051	40052	40053	40054	40055	40056	40057	40058	40059	40060
φ(n)	36300	17280	24336	17160	32040	13344	39040	20028	26700	16016

n	40061	40062	40063	40064	40065	40066	40067	40068	40069	40070
φ(n)	33408	12120	40062	19968	21360	17424	39576	11232	37696	16024

n	40071	40072	40073	40074	40075	40076	40077	40078	40079	40080
φ(n)	24624	20032	36420	13356	27360	19488	25920	19320	36984	10624

n	40081	40082	40083	40084	40085	40086	40087	40088	40089	40090
φ(n)	39664	17136	25800	18200	32064	12480	40086	20040	21648	15120

n	40091	40092	40093	40094	40095	40096	40097	40098	40099	40100
φ(n)	39192	12288	40092	20046	19440	17088	39600	12960	40098	16000

n	40101	40102	40103	40104	40105	40106	40107	40108	40109	40110
φ(n)	26732	20050	32256	13344	29568	18220	25760	19440	37980	9120

n	40111	40112	40113	40114	40115	40116	40117	40118	40119	40120
φ(n)	40110	19008	26736	19380	31360	13368	31200	18504	26040	14848

n	40121	40122	40123	40124	40125	40126	40127	40128	40129	40130
φ(n)	39312	13356	40122	17184	21200	20062	40126	11520	40128	16048

n	40131	40132	40133	40134	40135	40136	40137	40138	40139	40140
φ(n)	21168	19656	39468	13376	30624	19264	25152	16560	35200	10656

n	40141	40142	40143	40144	40145	40146	40147	40148	40149	40150
φ(n)	39712	20070	26760	18432	25920	13380	38016	20072	26748	14400

n	40151	40152	40153	40154	40155	40156	40157	40158	40159	40160
φ(n)	40150	11424	40152	18880	21408	20076	37056	12672	34416	16000

n	40161	40162	40163	40164	40165	40166	40167	40168	40169	40170
φ(n)	24320	19572	40162	13384	30912	16200	26772	20080	40168	9792

n	40171	40172	40173	40174	40175	40176	40177	40178	40179	40180
φ(n)	37536	18040	22944	19656	32120	12960	40176	20088	26216	13440

n	40181	40182	40183	40184	40185	40186	40187	40188	40189	40190
φ(n)	38412	12960	33600	20088	19872	19740	34440	12544	40188	16072

n	40191	40192	40193	40194	40195	40196	40197	40198	40199	40200
φ(n)	26792	19968	40192	10080	32152	18528	26796	19800	39480	10560

n	40201	40202	40203	40204	40205	40206	40207	40208	40209	40210
φ(n)	34452	20100	26784	18216	26880	13400	38880	17184	24720	16080

n	40211	40212	40213	40214	40215	40216	40217	40218	40219	40220
φ(n)	39624	13392	40212	20106	18336	18240	39780	13404	39096	16080

n	40221	40222	40223	40224	40225	40226	40227	40228	40229	40230
φ(n)	25920	14976	36288	13376	32160	20112	22880	19712	34440	10656

n	40231	40232	40233	40234	40235	40236	40237	40238	40239	40240
φ(n)	40230	19504	26820	20116	29664	11472	40236	17400	25152	16064

n	40241	40242	40243	40244	40245	40246	40247	40248	40249	40250
φ(n)	40240	12672	34488	20120	21456	20122	39840	12096	36580	13200

n	40251	40252	40253	40254	40255	40256	40257	40258	40259	40260
φ(n)	26832	19376	40252	13416	31488	18432	22680	20128	39816	9600

n	40261	40262	40263	40264	40265	40266	40267	40268	40269	40270
φ(n)	34992	19600	26840	17232	32208	13416	39600	20132	25920	16104

n	40271	40272	40273	40274	40275	40276	40277	40278	40279	40280
φ(n)	31320	13408	35904	18576	21360	20136	40276	11424	39376	14976

n	40281	40282	40283	40284	40285	40286	40287	40288	40289	40290
φ(n)	25872	18300	40282	13392	27600	20142	24768	20128	40288	9984

n	40291	40292	40293	40294	40295	40296	40297	40298	40299	40300
φ(n)	39312	17256	23760	20146	32232	12672	39556	20148	21600	14400

n	40301	40302	40303	40304	40305	40306	40307	40308	40309	40310
φ(n)	39900	13428	39280	18240	21488	17268	37920	13432	39904	15456

n	40311	40312	40313	40314	40315	40316	40317	40318	40319	40320
φ(n)	26856	20152	31824	13436	29280	20156	26400	19080	38544	9216

n	40321	40322	40323	40324	40325	40326	40327	40328	40329	40330
φ(n)	39600	20160	26880	18944	32240	11040	34524	19880	26880	15552

n	40331	40332	40333	40334	40335	40336	40337	40338	40339	40340
φ(n)	39000	13440	39520	16632	21504	20160	34560	13284	35616	16128

n	40341	40342	40343	40344	40345	40346	40347	40348	40349	40350
φ(n)	21504	19272	40342	13120	32272	20172	26892	15600	39936	10720

n	40351	40352	40353	40354	40355	40356	40357	40358	40359	40360
φ(n)	40350	18432	26900	20176	27648	12528	40356	18976	24440	16128

n	40361	40362	40363	40364	40365	40366	40367	40368	40369	40370
φ(n)	40360	11160	39960	20180	19008	20182	39240	12992	33696	14640

n	40371	40372	40373	40374	40375	40376	40377	40378	40379	40380
φ(n)	26912	20184	39468	13452	28800	17136	26208	18624	39960	10752

n	40381	40382	40383	40384	40385	40386	40387	40388	40389	40390
φ(n)	36700	19800	23040	20160	31360	13104	40386	19272	26924	13824

n	40391	40392	40393	40394	40395	40396	40397	40398	40399	40400
φ(n)	37128	11520	39060	19116	21536	20196	33264	13464	39760	16000

n	40401	40402	40403	40404	40405	40406	40407	40408	40409	40410
φ(n)	26532	20200	36720	10368	32320	19888	26936	20200	38016	10752

n	40411	40412	40413	40414	40415	40416	40417	40418	40419	40420
φ(n)	33000	20204	25488	18260	31552	13440	37296	17316	26892	15456

n	40421	40422	40423	40424	40425	40426	40427	40428	40429	40430
φ(n)	39852	13472	40422	19440	16800	17920	40426	13464	40428	14880

n	40431	40432	40433	40434	40435	40436	40437	40438	40439	40440
φ(n)	26952	16416	40432	12848	32344	18360	26952	20218	33696	10752

n	40441	40442	40443	40444	40445	40446	40447	40448	40449	40450
φ(n)	39312	19872	23040	20220	32352	11448	36760	19968	26496	16160

n	40451	40452	40453	40454	40455	40456	40457	40458	40459	40460
φ(n)	38304	13480	34668	19936	20160	18624	38676	12240	40458	13056

n	40461	40462	40463	40464	40465	40466	40467	40468	40469	40470
φ(n)	26972	20230	39480	13440	32368	20232	22080	19800	33840	10080

n	40471	40472	40473	40474	40475	40476	40477	40478	40479	40480
φ(n)	40470	20232	26964	17052	32360	13488	38080	19656	26520	14080

n	40481	40482	40483	40484	40485	40486	40487	40488	40489	40490
φ(n)	34692	12384	40482	19488	21584	19560	40486	11520	38340	16192

n	40491	40492	40493	40494	40495	40496	40497	40498	40499	40500
φ(n)	24480	19760	40492	12672	25344	20240	26996	20248	40498	10800

n	40501	40502	40503	40504	40505	40506	40507	40508	40509	40510
φ(n)	40000	15720	25784	19680	32400	13104	40506	17280	23112	16200

n	40511	40512	40513	40514	40515	40516	40517	40518	40519	40520
φ(n)	38112	13440	35280	19780	20736	17352	39180	13500	40518	16192

n	40521	40522	40523	40524	40525	40526	40527	40528	40529	40530
φ(n)	24912	20260	34692	12240	32400	19360	25272	18944	40528	9216

n	40531	40532	40533	40534	40535	40536	40537	40538	40539	40540
φ(n)	40530	20264	26448	18696	29040	13488	34740	20268	27024	16208

n	40541	40542	40543	40544	40545	40546	40547	40548	40549	40550
φ(n)	39900	12992	40542	17280	19968	17280	37416	12960	36960	16200

n	40551	40552	40553	40554	40555	40556	40557	40558	40559	40560
φ(n)	23160	19584	40068	13500	32440	20276	24560	17376	40558	9984

n	40561	40562	40563	40564	40565	40566	40567	40568	40569	40570
φ(n)	39652	19072	27036	20280	25920	13520	40096	18400	27044	16224

n	40571	40572	40573	40574	40575	40576	40577	40578	40579	40580
φ(n)	39144	11088	37440	20286	21600	20224	40576	13524	28800	16224

n	40581	40582	40583	40584	40585	40586	40587	40588	40589	40590
φ(n)	26892	19992	40582	12672	32464	15984	26568	19872	39456	9600

n	40591	40592	40593	40594	40595	40596	40597	40598	40599	40600
φ(n)	40590	19488	23184	20296	30976	12672	40596	19864	24912	13440

n	40601	40602	40603	40604	40605	40606	40607	40608	40609	40610
φ(n)	36900	13200	38448	20300	21648	19968	34800	13248	40608	15600

n	40611	40612	40613	40614	40615	40616	40617	40618	40619	40620
φ(n)	27072	16800	38208	11592	32488	20304	27072	19404	40200	10816

n	40621	40622	40623	40624	40625	40626	40627	40628	40629	40630
φ(n)	34776	19224	24600	20304	30000	12960	40626	17400	26096	15232

n	40631	40632	40633	40634	40635	40636	40637	40638	40639	40640
φ(n)	39600	13536	40228	18460	18144	20316	40636	12480	40638	16128

n	40641	40642	40643	40644	40645	40646	40647	40648	40649	40650
φ(n)	23760	17412	40128	13536	29520	20322	25472	20320	34836	10800

n	40651	40652	40653	40654	40655	40656	40657	40658	40659	40660
φ(n)	36192	20324	27096	20326	31648	10560	40176	19600	27104	15264

n	40661	40662	40663	40664	40665	40666	40667	40668	40669	40670
φ(n)	40032	13500	33696	16896	21680	20332	36960	13552	39996	13776

n	40671	40672	40673	40674	40675	40676	40677	40678	40679	40680
φ(n)	27108	19200	40128	13556	32520	20336	21312	18060	38520	10752

n	40681	40682	40683	40684	40685	40686	40687	40688	40689	40690
φ(n)	38272	20340	26600	17424	31824	13560	36960	20336	24480	14976

n	40691	40692	40693	40694	40695	40696	40697	40698	40699	40700
φ(n)	34872	13560	40692	20346	21696	20344	40696	10368	40698	14400

n	40701	40702	40703	40704	40705	40706	40707	40708	40709	40710
φ(n)	27132	19872	36000	13312	27888	20352	27132	20352	40708	10208

n	40711	40712	40713	40714	40715	40716	40717	40718	40719	40720
φ(n)	37000	17424	26400	20356	30592	12096	38556	20358	23184	16256

n	40721	40722	40723	40724	40725	40726	40727	40728	40729	40730
φ(n)	39732	12320	40320	20360	21600	17448	40296	13568	37440	16288

n	40731	40732	40733	40734	40735	40736	40737	40738	40739	40740
φ(n)	27152	19136	30360	12960	32584	19008	26352	20368	40738	9216

n	40741	40742	40743	40744	40745	40746	40747	40748	40749	40750
φ(n)	40300	18792	27108	18480	31360	13580	34920	19920	25024	16200

n	40751	40752	40753	40754	40755	40756	40757	40758	40759	40760
φ(n)	40750	13536	40180	16800	17280	19448	39936	13584	40758	16288

n	40761	40762	40763	40764	40765	40766	40767	40768	40769	40770
φ(n)	23256	20064	40762	13104	31440	17280	26712	16128	40020	10800

n	40771	40772	40773	40774	40775	40776	40777	40778	40779	40780
φ(n)	40770	20384	27180	18144	27840	13584	36960	20388	25872	16304

n	40781	40782	40783	40784	40785	40786	40787	40788	40789	40790
φ(n)	37632	11640	38368	20384	21744	20392	40786	12240	34956	16312

n	40791	40792	40793	40794	40795	40796	40797	40798	40799	40800
φ(n)	27192	20392	38304	12528	31680	16560	27180	20398	37080	10240

n	40801	40802	40803	40804	40805	40806	40807	40808	40809	40810
φ(n)	40800	19492	22176	20200	32640	13596	36288	20400	26640	12480

n	40811	40812	40813	40814	40815	40816	40817	40818	40819	40820
φ(n)	39672	12816	40812	20406	21744	20400	32928	13604	40818	14976

n	40821	40822	40823	40824	40825	40826	40827	40828	40829	40830
φ(n)	24720	20410	40822	11664	30800	20128	26280	19952	40828	10880

n	40831	40832	40833	40834	40835	40836	40837	40838	40839	40840
φ(n)	33048	17920	25056	19200	32664	13120	40320	17496	27224	16320

n	40841	40842	40843	40844	40845	40846	40847	40848	40849	40850
φ(n)	40840	13608	35880	20420	18624	18840	40846	12672	40848	15120

n	40851	40852	40853	40854	40855	40856	40857	40858	40859	40860
φ(n)	25344	17496	40852	12360	32680	20424	27236	19740	32256	10848

n	40861	40862	40863	40864	40865	40866	40867	40868	40869	40870
φ(n)	39424	20430	26624	20416	29680	11592	40866	19200	25704	15840

n	40871	40872	40873	40874	40875	40876	40877	40878	40879	40880
φ(n)	39072	12480	35028	20140	21600	18560	39840	13608	40878	13824

n	40881	40882	40883	40884	40885	40886	40887	40888	40889	40890
φ(n)	27252	20440	40882	13624	27648	20442	20880	19296	39540	10304

n	40891	40892	40893	40894	40895	40896	40897	40898	40899	40900
φ(n)	40392	20444	26544	16632	32712	13440	40896	17160	27264	16320

n	40901	40902	40903	40904	40905	40906	40907	40908	40909	40910
φ(n)	35052	12800	40902	20448	21600	20160	38736	11664	37180	16360

n	40911	40912	40913	40914	40915	40916	40917	40918	40919	40920
φ(n)	25152	20448	40500	13632	27888	19968	26048	19920	36736	9600

n	40921	40922	40923	40924	40925	40926	40927	40928	40929	40930
φ(n)	40500	16848	27276	18864	32720	12888	40926	20448	23376	16368

n	40931	40932	40933	40934	40935	40936	40937	40938	40939	40940
φ(n)	36600	13608	40932	20160	21824	16128	36432	13644	40938	15488

n	40941	40942	40943	40944	40945	40946	40947	40948	40949	40950
φ(n)	27288	18600	35088	13632	30960	20068	27296	19712	40948	8640

n	40951	40952	40953	40954	40955	40956	40957	40958	40959	40960
φ(n)	39600	20472	23040	20476	32760	13648	35100	20478	25920	16384

n	40961	40962	40963	40964	40965	40966	40967	40968	40969	40970
φ(n)	40960	13652	35904	15120	21840	20482	40320	13632	40144	15360

n	40971	40972	40973	40974	40975	40976	40977	40978	40979	40980
φ(n)	23400	20484	40972	13656	29600	18816	26208	17556	39984	10912

n	40981	40982	40983	40984	40985	40986	40987	40988	40989	40990
φ(n)	40492	19800	25848	19872	28080	11880	38560	20492	25200	16392

n	40991	40992	40993	40994	40995	40996	40997	40998	40999	41000
φ(n)	40584	11520	40992	20196	21840	19872	37260	13664	35136	16000

J.P. Martin-Flatin