]> Euler's Totient Function for n = 41001..42000

Euler's Totient Function for n = 41001..42000

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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	41001	41002	41003	41004	41005	41006	41007	41008	41009	41010
φ(n)	26832	17712	40560	12672	32016	16800	27336	18560	39204	10928

n	41011	41012	41013	41014	41015	41016	41017	41018	41019	41020
φ(n)	41010	20504	22680	20506	30240	13664	41016	20508	24640	14016

n	41021	41022	41023	41024	41025	41026	41027	41028	41029	41030
φ(n)	36288	13104	41022	20480	21840	20160	35160	12576	40480	14880

n	41031	41032	41033	41034	41035	41036	41037	41038	41039	41040
φ(n)	26496	19536	39888	11712	31584	20516	27356	19040	41038	10368

n	41041	41042	41043	41044	41045	41046	41047	41048	41049	41050
φ(n)	28800	20520	27360	19800	32832	13680	41046	17568	27360	16400

n	41051	41052	41053	41054	41055	41056	41057	41058	41059	41060
φ(n)	41050	12400	40320	18936	16896	20512	41056	13680	38880	16416

n	41061	41062	41063	41064	41065	41066	41067	41068	41069	41070
φ(n)	27372	17556	37320	12992	31920	20532	25272	20532	35196	10656

n	41071	41072	41073	41074	41075	41076	41077	41078	41079	41080
φ(n)	40392	19200	27380	18660	31200	11664	41076	18216	27384	14976

n	41081	41082	41083	41084	41085	41086	41087	41088	41089	41090
φ(n)	41080	13280	35208	20540	19680	20542	40680	13568	38656	14064

n	41091	41092	41093	41094	41095	41096	41097	41098	41099	41100
φ(n)	27392	20544	36288	13680	32872	18640	22032	20548	40464	10880

n	41101	41102	41103	41104	41105	41106	41107	41108	41109	41110
φ(n)	39292	20550	27396	17568	32880	11520	36000	19992	26880	16440

n	41111	41112	41113	41114	41115	41116	41117	41118	41119	41120
φ(n)	35196	13680	41112	20160	21920	19440	41116	10560	37944	16384

n	41121	41122	41123	41124	41125	41126	41127	41128	41129	41130
φ(n)	27396	19824	37120	13024	27600	20562	27416	19968	37380	10944

n	41131	41132	41133	41134	41135	41136	41137	41138	41139	41140
φ(n)	41130	16128	27420	20280	31104	13696	39780	20196	23472	14080

n	41141	41142	41143	41144	41145	41146	41147	41148	41149	41150
φ(n)	41140	13712	41142	19872	20160	17628	39336	13608	41148	16440

n	41151	41152	41153	41154	41155	41156	41157	41158	41159	41160
φ(n)	23520	20544	35268	12996	32920	20576	25728	18984	40560	9408

n	41161	41162	41163	41164	41165	41166	41167	41168	41169	41170
φ(n)	41160	18700	27440	20000	32928	13716	35280	19680	27444	15664

n	41171	41172	41173	41174	41175	41176	41177	41178	41179	41180
φ(n)	37992	13248	35280	16512	21600	20584	41176	13724	41178	15680

n	41181	41182	41183	41184	41185	41186	41187	41188	41189	41190
φ(n)	22464	20184	41182	11520	32944	20592	27456	17640	41188	10976

n	41191	41192	41193	41194	41195	41196	41197	41198	41199	41200
φ(n)	38752	19440	26136	20076	25440	13728	38016	20598	26520	16320

n	41201	41202	41203	41204	41205	41206	41207	41208	41209	41210
φ(n)	41200	11664	41202	20600	21120	18720	40656	12800	34104	15168

n	41211	41212	41213	41214	41215	41216	41217	41218	41219	41220
φ(n)	25920	20604	41212	13736	32968	16896	24960	20016	40296	10944

n	41221	41222	41223	41224	41225	41226	41227	41228	41229	41230
φ(n)	41220	20610	21600	20608	30720	13740	41226	18720	27432	12960

n	41231	41232	41233	41234	41235	41236	41237	41238	41239	41240
φ(n)	41230	13728	41232	20176	21984	18720	34272	13104	35640	16480

n	41241	41242	41243	41244	41245	41246	41247	41248	41249	41250
φ(n)	26912	19392	41242	11760	32256	20080	27492	20608	35856	10000

n	41251	41252	41253	41254	41255	41256	41257	41258	41259	41260
φ(n)	34440	20624	27500	20626	31968	13680	41256	17640	25856	16496

n	41261	41262	41263	41264	41265	41266	41267	41268	41269	41270
φ(n)	36300	12144	41262	20624	18720	20148	39816	12960	41268	16504

n	41271	41272	41273	41274	41275	41276	41277	41278	41279	41280
φ(n)	27512	15840	40848	13752	30240	19392	27516	20638	35376	10752

n	41281	41282	41283	41284	41285	41286	41287	41288	41289	41290
φ(n)	41280	20640	24840	20640	31504	11784	37440	19008	27524	16512

n	41291	41292	41293	41294	41295	41296	41297	41298	41299	41300
φ(n)	40872	12960	33216	18760	22016	19712	40560	13764	41298	13920

n	41301	41302	41303	41304	41305	41306	41307	41308	41309	41310
φ(n)	25344	20352	40800	13760	30000	19548	23520	19712	40800	10368

n	41311	41312	41313	41314	41315	41316	41317	41318	41319	41320
φ(n)	40824	20640	26864	16272	33048	12480	40716	20304	27540	16512

n	41321	41322	41323	41324	41325	41326	41327	41328	41329	41330
φ(n)	35412	13440	39060	20660	20160	20662	32640	11520	40176	16528

n	41331	41332	41333	41334	41335	41336	41337	41338	41339	41340
φ(n)	26312	20664	41332	13612	28320	20664	27540	18780	40656	9984

n	41341	41342	41343	41344	41345	41346	41347	41348	41349	41350
φ(n)	41340	17712	27560	18432	33072	13776	40936	20672	21360	16520

n	41351	41352	41353	41354	41355	41356	41357	41358	41359	41360
φ(n)	41350	13776	38160	18480	22032	17640	41356	13440	40600	14720

n	41361	41362	41363	41364	41365	41366	41367	41368	41369	41370
φ(n)	25920	20680	33480	13752	33088	18144	27576	20680	40320	9408

n	41371	41372	41373	41374	41375	41376	41377	41378	41379	41380
φ(n)	37600	20684	27576	20400	33000	13760	33792	19456	25440	16544

n	41381	41382	41383	41384	41385	41386	41387	41388	41389	41390
φ(n)	41380	11880	39928	17712	21120	20692	41386	13792	41388	16552

n	41391	41392	41393	41394	41395	41396	41397	41398	41399	41400
φ(n)	23328	19008	36400	13796	31104	20280	27596	17736	41398	10560

n	41401	41402	41403	41404	41405	41406	41407	41408	41409	41410
φ(n)	39204	20412	26784	18800	26208	13464	40480	20672	26712	16000

n	41411	41412	41413	41414	41415	41416	41417	41418	41419	41420
φ(n)	41410	10752	41412	20706	20000	19920	40836	12528	34560	15552

n	41421	41422	41423	41424	41425	41426	41427	41428	41429	41430
φ(n)	27612	20424	39600	13792	33120	16080	27612	20712	38976	11040

n	41431	41432	41433	41434	41435	41436	41437	41438	41439	41440
φ(n)	38232	20712	23664	20716	33144	13800	37660	20718	26136	13824

n	41441	41442	41443	41444	41445	41446	41447	41448	41449	41450
φ(n)	39984	13812	41442	19104	22032	18304	34200	12480	41040	16560

n	41451	41452	41453	41454	41455	41456	41457	41458	41459	41460
φ(n)	26880	20160	41452	11592	33160	20720	25488	19620	37680	11040

n	41461	41462	41463	41464	41465	41466	41467	41468	41469	41470
φ(n)	35532	20730	25920	20160	33168	13820	41466	17760	26400	13440

n	41471	41472	41473	41474	41475	41476	41477	41478	41479	41480
φ(n)	40992	13824	40788	20416	18720	20736	37584	13320	41478	15360

n	41481	41482	41483	41484	41485	41486	41487	41488	41489	41490
φ(n)	25080	17772	38280	13824	33184	20742	27656	20736	35556	11040

n	41491	41492	41493	41494	41495	41496	41497	41498	41499	41500
φ(n)	41490	17600	27660	20746	32256	10368	39040	20748	26208	16400

n	41501	41502	41503	41504	41505	41506	41507	41508	41509	41510
φ(n)	40572	13832	32340	20736	22128	20752	41506	13824	36720	14208

n	41511	41512	41513	41514	41515	41516	41517	41518	41519	41520
φ(n)	27200	20752	41512	11520	30096	20352	23688	20758	41518	11008

n	41521	41522	41523	41524	41525	41526	41527	41528	41529	41530
φ(n)	41520	19152	27680	17784	30000	13824	41080	19936	27216	16608

n	41531	41532	41533	41534	41535	41536	41537	41538	41539	41540
φ(n)	33408	13840	40480	19656	20160	18560	40896	11088	41538	15840

n	41541	41542	41543	41544	41545	41546	41547	41548	41549	41550
φ(n)	27120	20770	41542	13824	28464	20772	25160	17664	41548	11040

n	41551	41552	41553	41554	41555	41556	41557	41558	41559	41560
φ(n)	40392	17472	26244	20436	33240	13848	40096	18880	23736	16608

n	41561	41562	41563	41564	41565	41566	41567	41568	41569	41570
φ(n)	36432	13848	41008	20780	20736	17808	41160	13824	37780	16624

n	41571	41572	41573	41574	41575	41576	41577	41578	41579	41580
φ(n)	26640	19656	35628	12480	33240	20784	27716	20788	41578	8640

n	41581	41582	41583	41584	41585	41586	41587	41588	41589	41590
φ(n)	40572	19552	27224	19712	33264	13328	32832	20160	27720	16632

n	41591	41592	41593	41594	41595	41596	41597	41598	41599	41600
φ(n)	35640	13856	41592	17820	21344	20796	41596	13860	39136	15360

n	41601	41602	41603	41604	41605	41606	41607	41608	41609	41610
φ(n)	23688	18000	41602	13864	32448	20440	26136	17808	41608	10368

n	41611	41612	41613	41614	41615	41616	41617	41618	41619	41620
φ(n)	41610	20400	23040	20806	26880	13056	41616	20808	27744	16640

n	41621	41622	41623	41624	41625	41626	41627	41628	41629	41630
φ(n)	41620	11880	41128	18480	21600	19200	41626	13872	33696	15840

n	41631	41632	41633	41634	41635	41636	41637	41638	41639	41640
φ(n)	27752	20800	37440	13824	30240	17832	27756	20520	38424	11072

n	41641	41642	41643	41644	41645	41646	41647	41648	41649	41650
φ(n)	41640	20332	23760	20048	33312	12600	41646	19584	27764	13440

n	41651	41652	41653	41654	41655	41656	41657	41658	41659	41660
φ(n)	41650	12672	39820	20416	22208	20160	32400	13520	41658	16656

n	41661	41662	41663	41664	41665	41666	41667	41668	41669	41670
φ(n)	27756	20232	40920	11520	30720	20500	24192	18920	41668	11088

n	41671	41672	41673	41674	41675	41676	41677	41678	41679	41680
φ(n)	35712	20832	26768	20460	33320	13200	41020	16416	25200	16640

n	41681	41682	41683	41684	41685	41686	41687	41688	41689	41690
φ(n)	41680	13892	41040	19584	19008	19728	41686	13824	40756	15120

n	41691	41692	41693	41694	41695	41696	41697	41698	41699	41700
φ(n)	25632	17856	41280	13896	32160	20832	26880	20848	33264	11040

n	41701	41702	41703	41704	41705	41706	41707	41708	41709	41710
φ(n)	35520	20104	27800	19200	31536	11880	41296	20852	27804	16128

n	41711	41712	41713	41714	41715	41716	41717	41718	41719	41720
φ(n)	40872	12480	34800	20856	22032	20856	38496	13056	41718	14208

n	41721	41722	41723	41724	41725	41726	41727	41728	41729	41730
φ(n)	27812	19932	37920	12960	33360	20160	23832	20736	41728	10176

n	41731	41732	41733	41734	41735	41736	41737	41738	41739	41740
φ(n)	40264	20864	27816	16200	31360	13248	41736	20320	27824	16688

n	41741	41742	41743	41744	41745	41746	41747	41748	41749	41750
φ(n)	34848	13896	36504	20864	19360	20872	41256	11760	41164	16600

n	41751	41752	41753	41754	41755	41756	41757	41758	41759	41760
φ(n)	27828	19584	40740	13916	28608	17280	26880	20878	41758	10752

n	41761	41762	41763	41764	41765	41766	41767	41768	41769	41770
φ(n)	41760	16848	27840	20384	33408	13920	37960	19888	20736	16704

n	41771	41772	41773	41774	41775	41776	41777	41778	41779	41780
φ(n)	41770	13688	40608	20886	22240	17856	41776	12600	40720	16704

n	41781	41782	41783	41784	41785	41786	41787	41788	41789	41790
φ(n)	26352	19272	34776	13920	32640	19648	27852	20160	36400	9504

n	41791	41792	41793	41794	41795	41796	41797	41798	41799	41800
φ(n)	39468	20864	27860	20896	30816	13608	35784	20898	27864	14400

n	41801	41802	41803	41804	41805	41806	41807	41808	41809	41810
φ(n)	41800	13932	39328	17904	22272	20902	41280	12672	41808	16128

n	41811	41812	41813	41814	41815	41816	41817	41818	41819	41820
φ(n)	21600	20904	41812	13200	33448	20904	27248	17136	37800	10240

n	41821	41822	41823	41824	41825	41826	41827	41828	41829	41830
φ(n)	38592	19000	27864	20896	28560	13940	41400	20912	27360	16192

n	41831	41832	41833	41834	41835	41836	41837	41838	41839	41840
φ(n)	41064	11808	38020	19296	22304	20916	37312	13176	34776	16704

n	41841	41842	41843	41844	41845	41846	41847	41848	41849	41850
φ(n)	27888	20920	41842	12640	33472	17640	24192	20920	41848	10800

n	41851	41852	41853	41854	41855	41856	41857	41858	41859	41860
φ(n)	41850	20924	23904	19680	30400	13824	39636	20928	27900	12672

n	41861	41862	41863	41864	41865	41866	41867	41868	41869	41870
φ(n)	40800	13952	41862	20928	22320	18920	35880	13944	41440	16224

n	41871	41872	41873	41874	41875	41876	41877	41878	41879	41880
φ(n)	26240	20928	38640	11952	33000	19152	24840	20938	41878	11136

n	41881	41882	41883	41884	41885	41886	41887	41888	41889	41890
φ(n)	34560	20412	26664	20304	33504	12816	41886	15360	27924	16240

n	41891	41892	41893	41894	41895	41896	41897	41898	41899	41900
φ(n)	41472	13960	41892	20946	18144	20944	41896	13964	35040	16720

n	41901	41902	41903	41904	41905	41906	41907	41908	41909	41910
φ(n)	27932	17280	41902	13824	30464	20020	27360	20952	35916	10080

n	41911	41912	41913	41914	41915	41916	41917	41918	41919	41920
φ(n)	41910	18720	27936	19836	32800	11952	41500	20958	27456	16640

n	41921	41922	41923	41924	41925	41926	41927	41928	41929	41930
φ(n)	36720	13056	34944	20424	20160	20962	41926	13968	40084	14352

n	41931	41932	41933	41934	41935	41936	41937	41938	41939	41940
φ(n)	27936	19040	39708	13440	33544	20960	23952	19344	39456	11136

n	41941	41942	41943	41944	41945	41946	41947	41948	41949	41950
φ(n)	41940	20592	24000	17808	33552	13980	41946	20972	27144	16760

n	41951	41952	41953	41954	41955	41956	41957	41958	41959	41960
φ(n)	33120	12672	41952	19060	22368	19712	41956	11664	41958	16768

n	41961	41962	41963	41964	41965	41966	41967	41968	41969	41970
φ(n)	27440	20980	40488	12864	25920	20982	27972	20160	41968	11184

n	41971	41972	41973	41974	41975	41976	41977	41978	41979	41980
φ(n)	38916	17976	26304	20280	31680	12480	38736	20700	23976	16784

n	41981	41982	41983	41984	41985	41986	41987	41988	41989	41990
φ(n)	41980	13992	41982	20480	22320	17988	38060	13992	41580	13824

n	41991	41992	41993	41994	41995	41996	41997	41998	41999	42000
φ(n)	27992	20160	35952	13992	32544	20996	27996	18040	41998	9600

J.P. Martin-Flatin