]> Euler's Totient Function for n = 47001..48000

Euler's Totient Function for n = 47001..48000

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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	47001	47002	47003	47004	47005	47006	47007	47008	47009	47010
φ(n)	31332	23100	42720	15664	29952	22248	31320	21504	45360	12528

n	47011	47012	47013	47014	47015	47016	47017	47018	47019	47020
φ(n)	46072	19008	31340	21360	37608	15648	47016	23508	26856	18800

n	47021	47022	47023	47024	47025	47026	47027	47028	47029	47030
φ(n)	43392	14720	46168	23504	21600	20148	43200	15672	46540	18808

n	47031	47032	47033	47034	47035	47036	47037	47038	47039	47040
φ(n)	30720	23512	40308	14256	35904	21360	31356	22680	44256	10752

n	47041	47042	47043	47044	47045	47046	47047	47048	47049	47050
φ(n)	47040	22932	31356	22248	37248	15680	33120	23520	31364	18800

n	47051	47052	47053	47054	47055	47056	47057	47058	47059	47060
φ(n)	47050	15672	46620	20160	25088	22016	47056	13200	47058	17280

n	47061	47062	47063	47064	47065	47066	47067	47068	47069	47070
φ(n)	26568	23530	44568	14976	37648	23200	30240	19680	42680	12528

n	47071	47072	47073	47074	47075	47076	47077	47078	47079	47080
φ(n)	46512	23520	26880	23536	32160	15688	46636	23538	31380	16960

n	47081	47082	47083	47084	47085	47086	47087	47088	47089	47090
φ(n)	44528	12528	46648	23088	24192	21720	47086	15552	39060	17664

n	47091	47092	47093	47094	47095	47096	47097	47098	47099	47100
φ(n)	28520	23040	47092	15272	37672	19488	31392	23548	43464	12480

n	47101	47102	47103	47104	47105	47106	47107	47108	47109	47110
φ(n)	42768	21400	26904	22528	37680	15696	44064	23552	30560	16128

n	47111	47112	47113	47114	47115	47116	47117	47118	47119	47120
φ(n)	47110	14400	42820	23556	25056	23556	39312	15704	47118	17280

n	47121	47122	47123	47124	47125	47126	47127	47128	47129	47130
φ(n)	30912	23560	47122	11520	33600	23562	30008	22848	47128	12560

n	47131	47132	47133	47134	47135	47136	47137	47138	47139	47140
φ(n)	40392	23564	31416	23566	34240	15680	47136	18144	29736	18848

n	47141	47142	47143	47144	47145	47146	47147	47148	47149	47150
φ(n)	42688	15552	47142	22960	21504	21420	47146	15712	47148	17600

n	47151	47152	47153	47154	47155	47156	47157	47158	47159	47160
φ(n)	28080	20160	46320	15120	37720	23576	28560	20736	40416	12480

n	47161	47162	47163	47164	47165	47166	47167	47168	47169	47170
φ(n)	47160	23580	30888	21744	37728	13464	46600	21120	31428	18304

n	47171	47172	47173	47174	47175	47176	47177	47178	47179	47180
φ(n)	46032	15720	38544	23256	23040	23584	41040	15720	42880	16128

n	47181	47182	47183	47184	47185	47186	47187	47188	47189	47190
φ(n)	31452	22800	45528	15712	37744	23592	26712	23000	47188	10560

n	47191	47192	47193	47194	47195	47196	47197	47198	47199	47200
φ(n)	46000	22144	31460	20220	37752	14256	46656	23598	31464	18560

n	47201	47202	47203	47204	47205	47206	47207	47208	47209	47210
φ(n)	36720	15732	43560	23600	25152	23602	47206	13440	44416	18880

n	47211	47212	47213	47214	47215	47216	47217	47218	47219	47220
φ(n)	31472	20160	45660	15120	30240	21696	31476	23608	45144	12576

n	47221	47222	47223	47224	47225	47226	47227	47228	47229	47230
φ(n)	47220	20232	28080	23608	37760	14784	46576	23612	24768	18888

n	47231	47232	47233	47234	47235	47236	47237	47238	47239	47240
φ(n)	46512	15360	46768	20160	24288	20160	47236	15744	46656	18880

n	47241	47242	47243	47244	47245	47246	47247	47248	47249	47250
φ(n)	30240	20592	38016	15120	34320	23622	31496	23616	45936	10800

n	47251	47252	47253	47254	47255	47256	47257	47258	47259	47260
φ(n)	47250	23624	29808	23626	34848	14240	39312	23628	30624	17664

n	47261	47262	47263	47264	47265	47266	47267	47268	47269	47270
φ(n)	46812	15752	46800	20160	23936	23632	42960	14400	47268	18144

n	47271	47272	47273	47274	47275	47276	47277	47278	47279	47280
φ(n)	27000	22320	46080	15756	36000	23088	29376	18360	47278	12544

n	47281	47282	47283	47284	47285	47286	47287	47288	47289	47290
φ(n)	43632	23092	31520	23640	32256	15120	47286	22528	28640	18912

n	47291	47292	47293	47294	47295	47296	47297	47298	47299	47300
φ(n)	44460	13488	47292	20352	25200	23616	47296	15764	38976	16800

n	47301	47302	47303	47304	47305	47306	47307	47308	47309	47310
φ(n)	31532	23232	47302	15552	37840	19440	29088	23652	47308	11808

n	47311	47312	47313	47314	47315	47316	47317	47318	47319	47320
φ(n)	38720	23648	27000	23040	37848	15768	47316	23200	31544	14976

n	47321	47322	47323	47324	47325	47326	47327	47328	47329	47330
φ(n)	46644	14280	46008	23660	25200	23662	40560	14336	43056	18928

n	47331	47332	47333	47334	47335	47336	47337	47338	47339	47340
φ(n)	31536	23664	39600	12936	37864	23040	30480	23668	47338	12576

n	47341	47342	47343	47344	47345	47346	47347	47348	47349	47350
φ(n)	40572	23670	30744	21440	35584	14544	46816	19008	31560	18920

n	47351	47352	47353	47354	47355	47356	47357	47358	47359	47360
φ(n)	47350	15776	47352	23676	19200	23676	43120	15768	43704	18432

n	47361	47362	47363	47364	47365	47366	47367	47368	47369	47370
φ(n)	31572	19008	47362	15784	37888	21520	29808	22800	39600	12624

n	47371	47372	47373	47374	47375	47376	47377	47378	47379	47380
φ(n)	46872	21840	31580	23686	37800	13248	41760	23688	29696	17952

n	47381	47382	47383	47384	47385	47386	47387	47388	47389	47390
φ(n)	47380	15392	40572	23688	23328	21168	47386	14320	47388	16224

n	47391	47392	47393	47394	47395	47396	47397	47398	47399	47400
φ(n)	31592	23680	46740	15792	37912	21760	25920	21864	41400	12480

n	47401	47402	47403	47404	47405	47406	47407	47408	47409	47410
φ(n)	46852	23392	30096	20304	35856	15800	47406	23696	31604	17200

n	47411	47412	47413	47414	47415	47416	47417	47418	47419	47420
φ(n)	37440	15768	44608	23400	24192	23704	47416	13536	47418	18960

n	47421	47422	47423	47424	47425	47426	47427	47428	47429	47430
φ(n)	28680	23400	46368	13824	32400	22660	31616	23240	46284	11520

n	47431	47432	47433	47434	47435	47436	47437	47438	47439	47440
φ(n)	47430	18480	31104	23040	37024	15312	42240	23718	27000	18944

n	47441	47442	47443	47444	47445	47446	47447	47448	47449	47450
φ(n)	47440	15812	40680	22848	25296	20328	44640	15792	45364	17280

n	47451	47452	47453	47454	47455	47456	47457	47458	47459	47460
φ(n)	31632	23724	40668	14360	37960	23712	31632	23280	47458	10752

n	47461	47462	47463	47464	47465	47466	47467	47468	47469	47470
φ(n)	45900	22464	29184	22272	34480	15768	40680	23732	31644	18400

n	47471	47472	47473	47474	47475	47476	47477	47478	47479	47480
φ(n)	46152	14784	45808	20340	25200	19680	47040	15360	46800	18976

n	47481	47482	47483	47484	47485	47486	47487	47488	47489	47490
φ(n)	24192	23740	46920	15816	37984	23742	28760	19968	43680	12656

n	47491	47492	47493	47494	47495	47496	47497	47498	47499	47500
φ(n)	47490	22920	31644	23746	30624	15824	47496	20160	31080	18000

n	47501	47502	47503	47504	47505	47506	47507	47508	47509	47510
φ(n)	47500	12096	46728	23744	25328	23752	47506	15264	36960	19000

n	47511	47512	47513	47514	47515	47516	47517	47518	47519	47520
φ(n)	31668	23752	47512	15836	32256	20352	30912	22704	43200	11520

n	47521	47522	47523	47524	47525	47526	47527	47528	47529	47530
φ(n)	47520	23760	25920	23544	38000	15664	47526	21888	31680	16128

n	47531	47532	47533	47534	47535	47536	47537	47538	47539	47540
φ(n)	41440	14848	47532	23766	25344	23760	40740	14904	47056	19008

n	47541	47542	47543	47544	47545	47546	47547	47548	47549	47550
φ(n)	27456	21600	47542	13536	36864	23772	31644	23772	44736	12640

n	47551	47552	47553	47554	47555	47556	47557	47558	47559	47560
φ(n)	40752	23744	28600	20880	38040	15840	45036	19656	31160	17920

n	47561	47562	47563	47564	47565	47566	47567	47568	47569	47570
φ(n)	47124	15852	47562	20240	21600	22368	43896	15840	47568	18480

n	47571	47572	47573	47574	47575	47576	47577	47578	47579	47580
φ(n)	31200	20376	47040	15840	34400	22464	31716	23788	40740	11520

n	47581	47582	47583	47584	47585	47586	47587	47588	47589	47590
φ(n)	47580	23112	29760	23776	36720	12240	45496	23792	30576	19032

n	47591	47592	47593	47594	47595	47596	47597	47598	47599	47600
φ(n)	47590	15840	37584	23296	23904	23328	43260	15864	47598	15360

n	47601	47602	47603	47604	47605	47606	47607	47608	47609	47610
φ(n)	30240	23800	47160	15864	38080	21960	27192	21600	47608	12144

n	47611	47612	47613	47614	47615	47616	47617	47618	47619	47620
φ(n)	46552	23804	31088	19224	37312	15360	44800	22960	25920	19040

n	47621	47622	47623	47624	47625	47626	47627	47628	47629	47630
φ(n)	40812	15872	47622	23808	25200	23812	47040	13608	47628	17280

n	47631	47632	47633	47634	47635	47636	47637	47638	47639	47640
φ(n)	31752	21888	42768	14912	32640	23816	30888	23818	47638	12672

n	47641	47642	47643	47644	47645	47646	47647	47648	47649	47650
φ(n)	42000	19680	31760	23184	35136	15876	43680	23808	27216	19040

n	47651	47652	47653	47654	47655	47656	47657	47658	47659	47660
φ(n)	44832	13680	47652	23826	25344	19008	47656	14352	47658	19056

n	47661	47662	47663	47664	47665	47666	47667	47668	47669	47670
φ(n)	31772	23830	37080	15840	38128	23832	31776	22400	46944	10848

n	47671	47672	47673	47674	47675	47676	47677	47678	47679	47680
φ(n)	41472	23200	31776	21560	38120	15232	40572	23040	30360	18944

n	47681	47682	47683	47684	47685	47686	47687	47688	47689	47690
φ(n)	47680	15876	46480	18720	21760	23520	46536	15888	47124	18000

n	47691	47692	47693	47694	47695	47696	47697	47698	47699	47700
φ(n)	27216	23844	46368	15896	38152	21600	29328	20436	47698	12480

n	47701	47702	47703	47704	47705	47706	47707	47708	47709	47710
φ(n)	47700	21120	31800	23232	30912	15900	43360	23852	29160	17568

n	47711	47712	47713	47714	47715	47716	47717	47718	47719	47720
φ(n)	47710	13440	47712	23856	25440	23400	47716	14400	38400	19072

n	47721	47722	47723	47724	47725	47726	47727	47728	47729	47730
φ(n)	31812	23532	44040	15360	36080	20412	31812	22464	43380	12096

n	47731	47732	47733	47734	47735	47736	47737	47738	47739	47740
φ(n)	46864	23864	27264	23016	38184	13824	47736	23868	31824	14400

n	47741	47742	47743	47744	47745	47746	47747	47748	47749	47750
φ(n)	47740	15552	47742	23808	25440	23872	38664	15136	44064	19000

n	47751	47752	47753	47754	47755	47756	47757	47758	47759	47760
φ(n)	28920	23184	44096	13608	38200	23876	31836	23878	47304	12672

n	47761	47762	47763	47764	47765	47766	47767	47768	47769	47770
φ(n)	40932	19920	30240	23880	37120	15048	46440	20448	31844	17920

n	47771	47772	47773	47774	47775	47776	47777	47778	47779	47780
φ(n)	43560	15912	42000	23886	20160	23872	47776	15924	47778	19104

n	47781	47782	47783	47784	47785	47786	47787	47788	47789	47790
φ(n)	31848	20472	47040	14400	36144	23892	29952	22032	40956	12528

n	47791	47792	47793	47794	47795	47796	47797	47798	47799	47800
φ(n)	47790	22848	31328	22836	34320	13632	47796	23898	30912	19040

n	47801	47802	47803	47804	47805	47806	47807	47808	47809	47810
φ(n)	44112	15360	40968	20736	25488	20800	47806	15744	47808	16368

n	47811	47812	47813	47814	47815	47816	47817	47818	47819	47820
φ(n)	31872	23904	47328	14688	37440	23184	23760	23908	47818	12736

n	47821	47822	47823	47824	47825	47826	47827	47828	47829	47830
φ(n)	43008	23910	30168	20160	38240	15936	43992	21720	31376	19128

n	47831	47832	47833	47834	47835	47836	47837	47838	47839	47840
φ(n)	40992	15936	46260	23916	25488	23916	47836	12672	43480	16896

n	47841	47842	47843	47844	47845	47846	47847	47848	47849	47850
φ(n)	30960	22644	47842	15912	32784	23368	31040	23920	46980	11200

n	47851	47852	47853	47854	47855	47856	47857	47858	47859	47860
φ(n)	47304	20496	29376	23520	35968	15936	47856	23928	26208	19136

n	47861	47862	47863	47864	47865	47866	47867	47868	47869	47870
φ(n)	41040	15948	45760	23040	25520	18864	47400	15952	47868	19144

n	47871	47872	47873	47874	47875	47876	47877	47878	47879	47880
φ(n)	31752	20480	40992	15600	38200	23936	31916	23256	42336	10368

n	47881	47882	47883	47884	47885	47886	47887	47888	47889	47890
φ(n)	47880	23584	29000	23940	37440	15224	41040	23040	29952	19152

n	47891	47892	47893	47894	47895	47896	47897	47898	47899	47900
φ(n)	47232	14688	46828	18600	24480	23944	47460	15948	45360	19120

n	47901	47902	47903	47904	47905	47906	47907	47908	47909	47910
φ(n)	27360	23352	47902	15936	31680	22528	31932	19488	45804	12768

n	47911	47912	47913	47914	47915	47916	47917	47918	47919	47920
φ(n)	47910	23296	31940	23956	31968	14520	47916	20736	31944	19136

n	47921	47922	47923	47924	47925	47926	47927	47928	47929	47930
φ(n)	47472	13608	45088	23960	25200	23160	43560	15968	39840	19168

n	47931	47932	47933	47934	47935	47936	47937	47938	47939	47940
φ(n)	29472	22880	47932	15972	38344	20352	29232	21780	47938	11776

n	47941	47942	47943	47944	47945	47946	47947	47948	47949	47950
φ(n)	47500	23970	27360	22080	37296	15600	47946	23972	29040	16320

n	47951	47952	47953	47954	47955	47956	47957	47958	47959	47960
φ(n)	47950	15552	47268	23976	24288	22680	34560	15984	47520	17280

n	47961	47962	47963	47964	47965	47966	47967	47968	47969	47970
φ(n)	31536	23980	47962	13680	37440	23128	31320	23968	47968	11520

n	47971	47972	47973	47974	47975	47976	47977	47978	47979	47980
φ(n)	36960	23496	31980	22304	36000	15984	47976	19536	31968	19184

n	47981	47982	47983	47984	47985	47986	47987	47988	47989	47990
φ(n)	47980	14520	44280	23984	21888	23992	46920	15120	46656	19192

n	47991	47992	47993	47994	47995	47996	47997	47998	47999	48000
φ(n)	30080	20544	43620	15120	36960	21840	31992	23664	41136	12800

J.P. Martin-Flatin