]> Euler's Totient Function for n = 46001..47000

Euler's Totient Function for n = 46001..47000

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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	46001	46002	46003	46004	46005	46006	46007	46008	46009	46010
φ(n)	45552	12800	45568	18720	24528	23002	42456	15120	45540	17808

n	46011	46012	46013	46014	46015	46016	46017	46018	46019	46020
φ(n)	26208	23004	40480	15336	36808	22976	30672	18576	43296	11136

n	46021	46022	46023	46024	46025	46026	46027	46028	46029	46030
φ(n)	46020	23010	28336	20880	31440	15336	46026	22320	30096	18408

n	46031	46032	46033	46034	46035	46036	46037	46038	46039	46040
φ(n)	45600	13056	42480	23016	21600	21632	43596	15344	39456	18400

n	46041	46042	46043	46044	46045	46046	46047	46048	46049	46050
φ(n)	30192	23020	44880	15336	36832	15840	30696	23008	46048	12240

n	46051	46052	46053	46054	46055	46056	46057	46058	46059	46060
φ(n)	46050	22176	24192	23026	36000	14400	40560	23028	28320	15456

n	46061	46062	46063	46064	46065	46066	46067	46068	46069	46070
φ(n)	46060	15336	45360	23024	23616	22260	39480	13920	44044	17280

n	46071	46072	46073	46074	46075	46076	46077	46078	46079	46080
φ(n)	30708	21216	46072	13152	34560	23036	30716	23038	40600	12288

n	46081	46082	46083	46084	46085	46086	46087	46088	46089	46090
φ(n)	37968	23040	30720	22400	33984	15360	43360	19728	30672	16720

n	46091	46092	46093	46094	46095	46096	46097	46098	46099	46100
φ(n)	46090	14608	46092	21816	21024	22176	44580	14112	46098	18400

n	46101	46102	46103	46104	46105	46106	46107	46108	46109	46110
φ(n)	27720	19008	46102	14336	36880	23052	29808	23052	39480	11648

n	46111	46112	46113	46114	46115	46116	46117	46118	46119	46120
φ(n)	42552	20800	29088	23056	35200	12960	45580	23058	30744	18432

n	46121	46122	46123	46124	46125	46126	46127	46128	46129	46130
φ(n)	43392	15372	35880	21264	24000	23062	45696	14880	45684	15792

n	46131	46132	46133	46134	46135	46136	46137	46138	46139	46140
φ(n)	30752	21816	46132	13920	36904	22464	24336	20416	42336	12288

n	46141	46142	46143	46144	46145	46146	46147	46148	46149	46150
φ(n)	46140	23070	30744	19584	33520	15380	46146	22632	30764	16800

n	46151	46152	46153	46154	46155	46156	46157	46158	46159	46160
φ(n)	37368	15360	46152	22540	23040	20960	45600	13104	44640	18432

n	46161	46162	46163	46164	46165	46166	46167	46168	46169	46170
φ(n)	29304	23080	41184	15384	31632	22480	27960	22176	45696	11664

n	46171	46172	46173	46174	46175	46176	46177	46178	46179	46180
φ(n)	46170	18432	30780	23086	36920	13824	45360	20980	26352	18464

n	46181	46182	46183	46184	46185	46186	46187	46188	46189	46190
φ(n)	46180	14952	46182	22000	24624	19788	46186	15384	34560	17760

n	46191	46192	46193	46194	46195	46196	46197	46198	46199	46200
φ(n)	30272	23088	39588	15396	36952	23096	29232	23098	46198	9600

n	46201	46202	46203	46204	46205	46206	46207	46208	46209	46210
φ(n)	45172	21312	30800	23100	36960	14400	36960	21888	30240	18480

n	46211	46212	46213	46214	46215	46216	46217	46218	46219	46220
φ(n)	42000	15400	44928	19800	22464	22464	45696	15404	46218	18480

n	46221	46222	46223	46224	46225	46226	46227	46228	46229	46230
φ(n)	25200	20900	43488	15264	36120	22288	29160	18144	46228	11616

n	46231	46232	46233	46234	46235	46236	46237	46238	46239	46240
φ(n)	45592	23112	27960	23116	31680	15408	46236	22680	30824	17408

n	46241	46242	46243	46244	46245	46246	46247	46248	46249	46250
φ(n)	42672	13176	45760	21000	24656	21888	45696	14720	39636	18000

n	46251	46252	46253	46254	46255	46256	46257	46258	46259	46260
φ(n)	30780	22320	44220	14208	32480	19488	28992	22800	45816	12288

n	46261	46262	46263	46264	46265	46266	46267	46268	46269	46270
φ(n)	46260	23130	26424	23128	34992	14000	42696	22512	29952	15840

n	46271	46272	46273	46274	46275	46276	46277	46278	46279	46280
φ(n)	46270	15360	46272	21760	24640	22088	36000	15408	46278	16896

n	46281	46282	46283	46284	46285	46286	46287	46288	46289	46290
φ(n)	30852	22752	44760	12096	37024	23142	29808	20960	45120	12336

n	46291	46292	46293	46294	46295	46296	46297	46298	46299	46300
φ(n)	37248	22680	28464	22776	36064	15408	45540	19836	26400	18480

n	46301	46302	46303	46304	46305	46306	46307	46308	46309	46310
φ(n)	46300	15432	43848	23136	21168	21216	46306	14464	46308	16800

n	46311	46312	46313	46314	46315	46316	46317	46318	46319	46320
φ(n)	30072	19824	44688	14760	36192	23156	30876	23158	36576	12288

n	46321	46322	46323	46324	46325	46326	46327	46328	46329	46330
φ(n)	42100	20592	30876	22464	34560	13224	46326	23160	30884	17920

n	46331	46332	46333	46334	46335	46336	46337	46338	46339	46340
φ(n)	45792	12960	39708	23166	24704	23040	46336	15444	45880	15840

n	46341	46342	46343	46344	46345	46346	46347	46348	46349	46350
φ(n)	29160	20608	42020	15440	31680	23172	26472	23172	46348	12240

n	46351	46352	46353	46354	46355	46356	46357	46358	46359	46360
φ(n)	46350	23168	30900	17640	36288	15448	45900	21384	28800	17280

n	46361	46362	46363	46364	46365	46366	46367	46368	46369	46370
φ(n)	38448	15452	45640	22704	22400	22848	45936	12672	45760	18544

n	46371	46372	46373	46374	46375	46376	46377	46378	46379	46380
φ(n)	26880	23184	45708	15080	31200	19200	30912	23188	43920	12352

n	46381	46382	46383	46384	46385	46386	46387	46388	46389	46390
φ(n)	46380	19872	30920	21312	37104	15444	42160	23192	25944	18552

n	46391	46392	46393	46394	46395	46396	46397	46398	46399	46400
φ(n)	44352	15456	43648	23196	24720	19872	41328	12960	46398	17920

n	46401	46402	46403	46404	46405	46406	46407	46408	46409	46410
φ(n)	30932	23200	39732	15456	37120	23202	29880	23200	42180	9216

n	46411	46412	46413	46414	46415	46416	46417	46418	46419	46420
φ(n)	46410	22560	30780	22176	37128	15456	37584	23208	30944	16800

n	46421	46422	46423	46424	46425	46426	46427	46428	46429	46430
φ(n)	45600	15468	42840	19872	24720	22908	43680	14976	44800	18568

n	46431	46432	46433	46434	46435	46436	46437	46438	46439	46440
φ(n)	23760	23200	45588	15120	36000	19872	29568	19080	46438	12096

n	46441	46442	46443	46444	46445	46446	46447	46448	46449	46450
φ(n)	46440	21100	30464	21824	31824	15480	46446	23216	28512	18560

n	46451	46452	46453	46454	46455	46456	46457	46458	46459	46460
φ(n)	46450	13104	40800	23226	23328	23224	46456	14784	39816	17600

n	46461	46462	46463	46464	46465	46466	46467	46468	46469	46470
φ(n)	29120	21432	45888	14080	37168	19908	30960	23232	44940	12384

n	46471	46472	46473	46474	46475	46476	46477	46478	46479	46480
φ(n)	46470	22464	26544	21996	31200	15480	46476	21856	30984	15744

n	46481	46482	46483	46484	46485	46486	46487	46488	46489	46490
φ(n)	45552	15120	42504	23240	24768	21120	38304	14208	46488	18592

n	46491	46492	46493	46494	46495	46496	46497	46498	46499	46500
φ(n)	30992	22736	44028	12960	34944	23232	28160	22836	46498	12000

n	46501	46502	46503	46504	46505	46506	46507	46508	46509	46510
φ(n)	36288	23250	30996	23248	36400	14784	46506	18000	30096	18600

n	46511	46512	46513	46514	46515	46516	46517	46518	46519	46520
φ(n)	46510	13824	46080	21456	21216	22400	46080	15504	42280	18592

n	46521	46522	46523	46524	46525	46526	46527	46528	46529	46530
φ(n)	30996	19932	46522	15504	37200	22680	28608	23232	35904	11040

n	46531	46532	46533	46534	46535	46536	46537	46538	46539	46540
φ(n)	42120	23264	31020	22776	36160	13248	46096	23268	31020	17088

n	46541	46542	46543	46544	46545	46546	46547	46548	46549	46550
φ(n)	42300	15512	38880	23264	23744	21312	45936	15480	46548	15120

n	46551	46552	46553	46554	46555	46556	46557	46558	46559	46560
φ(n)	30392	20240	42960	15516	37240	22848	26568	23278	46558	12288

n	46561	46562	46563	46564	46565	46566	46567	46568	46569	46570
φ(n)	46000	22500	26240	19944	36432	14256	46566	23280	28728	18624

n	46571	46572	46573	46574	46575	46576	46577	46578	46579	46580
φ(n)	39912	15520	46572	20160	23760	22400	45540	13296	42984	17408

n	46581	46582	46583	46584	46585	46586	46587	46588	46589	46590
φ(n)	31052	23290	45288	15504	29040	23292	30368	22032	46588	12416

n	46591	46592	46593	46594	46595	46596	46597	46598	46599	46600
φ(n)	46590	18432	29880	23296	37272	14080	43840	22264	26544	18560

n	46601	46602	46603	46604	46605	46606	46607	46608	46609	46610
φ(n)	46600	15516	44968	22800	22848	19968	39960	15520	46116	18096

n	46611	46612	46613	46614	46615	46616	46617	46618	46619	46620
φ(n)	31068	22680	39948	14592	37288	23304	30240	19440	46618	10368

n	46621	46622	46623	46624	46625	46626	46627	46628	46629	46630
φ(n)	44572	23310	31080	22080	37200	14688	39960	23312	28080	18648

n	46631	46632	46633	46634	46635	46636	46637	46638	46639	46640
φ(n)	40320	14784	46632	19980	24864	22880	46176	15540	46638	16640

n	46641	46642	46643	46644	46645	46646	46647	46648	46649	46650
φ(n)	26640	23320	46642	13728	35280	22960	30240	18816	46648	12400

n	46651	46652	46653	46654	46655	46656	46657	46658	46659	46660
φ(n)	42400	22896	31100	23326	30240	15552	41472	22720	30600	18656

n	46661	46662	46663	46664	46665	46666	46667	46668	46669	46670
φ(n)	45024	12000	46662	22032	23040	23332	44616	15552	38976	17184

n	46671	46672	46673	46674	46675	46676	46677	46678	46679	46680
φ(n)	30360	23328	42420	15552	37320	19992	31116	23338	46678	12416

n	46681	46682	46683	46684	46685	46686	46687	46688	46689	46690
φ(n)	46680	21952	23328	21200	37344	15000	46686	23328	30576	14784

n	46691	46692	46693	46694	46695	46696	46697	46698	46699	46700
φ(n)	46690	15552	45760	22680	22560	21504	39984	15120	42240	18640

n	46701	46702	46703	46704	46705	46706	46707	46708	46709	46710
φ(n)	31128	22104	46702	13248	37360	21120	31136	23352	43104	12384

n	46711	46712	46713	46714	46715	46716	46717	46718	46719	46720
φ(n)	40032	23352	29744	23356	37368	14592	40800	19320	29904	18432

n	46721	46722	46723	46724	46725	46726	46727	46728	46729	46730
φ(n)	44244	14352	46722	23360	21120	22920	46726	13920	46084	18688

n	46731	46732	46733	46734	46735	46736	46737	46738	46739	46740
φ(n)	30240	20016	43968	15576	34464	22176	31104	23368	36360	11520

n	46741	46742	46743	46744	46745	46746	46747	46748	46749	46750
φ(n)	45612	23370	31160	23368	37392	13104	46746	20160	31164	16000

n	46751	46752	46753	46754	46755	46756	46757	46758	46759	46760
φ(n)	46750	15552	40068	23040	24912	23376	46756	15584	41976	15936

n	46761	46762	46763	46764	46765	46766	46767	46768	46769	46770
φ(n)	25920	23052	46200	15552	36432	22968	24960	22464	46768	12464

n	46771	46772	46773	46774	46775	46776	46777	46778	46779	46780
φ(n)	46770	21240	31176	18432	37400	15584	45136	22140	30120	18704

n	46781	46782	46783	46784	46785	46786	46787	46788	46789	46790
φ(n)	38880	14784	42520	21504	24944	23088	41760	13344	46060	18712

n	46791	46792	46793	46794	46795	46796	46797	46798	46799	46800
φ(n)	31176	23392	46080	14160	31920	23396	29520	23398	45864	11520

n	46801	46802	46803	46804	46805	46806	46807	46808	46809	46810
φ(n)	44032	20052	31200	23400	31680	15008	46806	23400	26712	18000

n	46811	46812	46813	46814	46815	46816	46817	46818	46819	46820
φ(n)	46810	15088	43056	23056	24960	17280	46816	14688	46818	18720

n	46821	46822	46823	46824	46825	46826	46827	46828	46829	46830
φ(n)	31212	22800	40128	15600	37440	21600	27720	22352	46828	10656

n	46831	46832	46833	46834	46835	46836	46837	46838	46839	46840
φ(n)	46830	23408	30624	23416	32256	15600	40140	21280	28800	18720

n	46841	46842	46843	46844	46845	46846	46847	46848	46849	46850
φ(n)	45300	15120	46368	19992	24912	22968	46176	15360	42580	18720

n	46851	46852	46853	46854	46855	46856	46857	46858	46859	46860
φ(n)	25344	19968	46852	14688	37480	23424	31236	20076	45816	11200

n	46861	46862	46863	46864	46865	46866	46867	46868	46869	46870
φ(n)	46860	23430	30240	22400	29376	15264	46866	23432	29376	18144

n	46871	46872	46873	46874	46875	46876	46877	46878	46879	46880
φ(n)	42600	12960	44388	22396	25000	23436	46876	14400	38880	18688

n	46881	46882	46883	46884	46885	46886	46887	46888	46889	46890
φ(n)	31248	21300	46440	15624	37504	18816	31256	23440	46888	12480

n	46891	46892	46893	46894	46895	46896	46897	46898	46899	46900
φ(n)	43272	22176	23520	23446	36736	15616	44836	23140	31104	15840

n	46901	46902	46903	46904	46905	46906	46907	46908	46909	46910
φ(n)	46900	15632	42240	19200	24128	22908	40200	15624	46080	18760

n	46911	46912	46913	46914	46915	46916	46917	46918	46919	46920
φ(n)	29592	23424	45780	13392	34080	22752	28800	23458	46918	11264

n	46921	46922	46923	46924	46925	46926	46927	46928	46929	46930
φ(n)	40212	22624	31280	23460	37520	14040	46480	20064	31284	16416

n	46931	46932	46933	46934	46935	46936	46937	46938	46939	46940
φ(n)	46200	15640	46932	22680	21312	23464	40000	15644	46224	18768

n	46941	46942	46943	46944	46945	46946	46947	46948	46949	46950
φ(n)	31292	20076	41184	15552	36480	23472	31296	21120	38016	12480

n	46951	46952	46953	46954	46955	46956	46957	46958	46959	46960
φ(n)	45304	23472	29808	22080	37560	12096	46956	22984	28440	18752

n	46961	46962	46963	46964	46965	46966	46967	46968	46969	46970
φ(n)	46500	15648	40248	22968	24000	22440	46200	14688	43344	14400

n	46971	46972	46973	46974	46975	46976	46977	46978	46979	46980
φ(n)	29376	23484	46428	15656	37560	23424	26832	23124	46440	12096

n	46981	46982	46983	46984	46985	46986	46987	46988	46989	46990
φ(n)	42700	21528	31320	20112	37584	15200	44496	22080	29832	18144

n	46991	46992	46993	46994	46995	46996	46997	46998	46999	47000
φ(n)	39984	14080	46992	23496	23040	22680	46996	13392	45864	18400

J.P. Martin-Flatin