]> Euler's Totient Function for n = 29001..30000

Euler's Totient Function for n = 29001..30000

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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	29001	29002	29003	29004	29005	29006	29007	29008	29009	29010
φ(n)	16560	13632	25344	9664	23200	14502	17520	12096	29008	7728

n	29011	29012	29013	29014	29015	29016	29017	29018	29019	29020
φ(n)	28512	14504	18288	14256	19872	8640	29016	13180	18176	11600

n	29021	29022	29023	29024	29025	29026	29027	29028	29029	29030
φ(n)	29020	8280	29022	14496	15120	13860	29026	9280	20160	11608

n	29031	29032	29033	29034	29035	29036	29037	29038	29039	29040
φ(n)	19352	13680	29032	9672	23224	11520	19356	14518	28560	7040

n	29041	29042	29043	29044	29045	29046	29047	29048	29049	29050
φ(n)	28672	13392	16560	14144	22464	9384	28080	14520	18480	9840

n	29051	29052	29053	29054	29055	29056	29057	29058	29059	29060
φ(n)	24840	9648	27328	14256	14208	14464	24864	9296	29058	11616

n	29061	29062	29063	29064	29065	29066	29067	29068	29069	29070
φ(n)	19368	13200	29062	8256	23248	14532	19376	13104	28320	6912

n	29071	29072	29073	29074	29075	29076	29077	29078	29079	29080
φ(n)	24912	13728	17600	14536	23240	9688	29076	11880	19332	11616

n	29081	29082	29083	29084	29085	29086	29087	29088	29089	29090
φ(n)	26832	9360	28728	13200	13248	14542	25984	9600	27540	11632

n	29091	29092	29093	29094	29095	29096	29097	29098	29099	29100
φ(n)	19392	12456	28428	8928	20240	14544	18720	14548	24936	7680

n	29101	29102	29103	29104	29105	29106	29107	29108	29109	29110
φ(n)	29100	14550	19008	13568	23280	7560	26856	13752	18720	11200

n	29111	29112	29113	29114	29115	29116	29117	29118	29119	29120
φ(n)	28392	9696	24948	14556	15504	14000	26460	9240	28296	9216

n	29121	29122	29123	29124	29125	29126	29127	29128	29129	29130
φ(n)	18240	14560	29122	9696	23200	14562	15552	13200	29128	7760

n	29131	29132	29133	29134	29135	29136	29137	29138	29139	29140
φ(n)	29130	14564	17712	12480	23304	9696	29136	13696	17640	11040

n	29141	29142	29143	29144	29145	29146	29147	29148	29149	29150
φ(n)	23760	9708	28800	14568	14784	12528	29146	8304	28764	10400

n	29151	29152	29153	29154	29155	29156	29157	29158	29159	29160
φ(n)	18720	14560	29152	9408	18816	14112	19436	14280	26904	7776

n	29161	29162	29163	29164	29165	29166	29167	29168	29169	29170
φ(n)	26400	12492	19440	13904	22032	9720	29166	14576	16632	11664

n	29171	29172	29173	29174	29175	29176	29177	29178	29179	29180
φ(n)	28200	7680	29172	14056	15520	12480	28836	9720	29178	11664

n	29181	29182	29183	29184	29185	29186	29187	29188	29189	29190
φ(n)	19040	14590	22680	9216	21504	14592	18216	14592	27200	6624

n	29191	29192	29193	29194	29195	29196	29197	29198	29199	29200
φ(n)	29190	14080	18864	13260	23352	9720	24192	13464	19464	11520

n	29201	29202	29203	29204	29205	29206	29207	29208	29209	29210
φ(n)	29200	9360	26208	12432	13920	13728	29206	9728	29208	11088

n	29211	29212	29213	29214	29215	29216	29217	29218	29219	29220
φ(n)	15264	14256	28860	9720	23368	13120	19476	12516	28680	7776

n	29221	29222	29223	29224	29225	29226	29227	29228	29229	29230
φ(n)	29220	13824	18240	13440	19920	9740	26560	14612	19484	11232

n	29231	29232	29233	29234	29235	29236	29237	29238	29239	29240
φ(n)	29230	8064	26400	14260	15584	14616	26832	8840	25056	10752

n	29241	29242	29243	29244	29245	29246	29247	29248	29249	29250
φ(n)	18468	14620	29242	9744	23392	12528	19496	14592	26580	7200

n	29251	29252	29253	29254	29255	29256	29257	29258	29259	29260
φ(n)	29250	14280	16632	14626	23400	9152	27520	14628	19500	8640

n	29261	29262	29263	29264	29265	29266	29267	29268	29269	29270
φ(n)	28224	9752	27000	13920	15600	14632	24192	9720	29268	11704

n	29271	29272	29273	29274	29275	29276	29277	29278	29279	29280
φ(n)	17720	14632	28800	7680	23400	13488	19512	14638	26136	7680

n	29281	29282	29283	29284	29285	29286	29287	29288	29289	29290
φ(n)	24288	13310	18984	14640	23424	9756	29286	12528	18000	11200

n	29291	29292	29293	29294	29295	29296	29297	29298	29299	29300
φ(n)	27552	9760	26620	14400	12960	14640	29296	9216	28864	11680

n	29301	29302	29303	29304	29305	29306	29307	29308	29309	29310
φ(n)	19532	11088	29302	8640	23440	14652	19536	13760	24336	7808

n	29311	29312	29313	29314	29315	29316	29317	29318	29319	29320
φ(n)	29310	14592	19536	14656	19200	8352	27756	14416	18816	11712

n	29321	29322	29323	29324	29325	29326	29327	29328	29329	29330
φ(n)	28944	9720	24360	14660	14080	12600	29326	8832	28980	10032

n	29331	29332	29333	29334	29335	29336	29337	29338	29339	29340
φ(n)	19548	14664	29332	9776	23464	13824	15120	14668	29338	7776

n	29341	29342	29343	29344	29345	29346	29347	29348	29349	29350
φ(n)	25920	13792	19560	12480	23472	9504	29346	12320	19548	11720

n	29351	29352	29353	29354	29355	29356	29357	29358	29359	29360
φ(n)	25116	9776	29008	13536	14688	14240	28380	8352	24960	11712

n	29361	29362	29363	29364	29365	29366	29367	29368	29369	29370
φ(n)	19572	14352	29362	9784	20112	14682	18000	14680	28644	7040

n	29371	29372	29373	29374	29375	29376	29377	29378	29379	29380
φ(n)	28072	12576	19580	13896	23000	9216	28336	14256	16776	10752

n	29381	29382	29383	29384	29385	29386	29387	29388	29389	29390
φ(n)	26700	9512	29382	14688	15648	12588	29386	9360	29388	11752

n	29391	29392	29393	29394	29395	29396	29397	29398	29399	29400
φ(n)	19200	13280	20736	9240	23512	14696	19040	14698	29398	6720

n	29401	29402	29403	29404	29405	29406	29407	29408	29409	29410
φ(n)	29400	14400	17820	14700	23520	8736	25200	14688	19604	11008

n	29411	29412	29413	29414	29415	29416	29417	29418	29419	29420
φ(n)	29410	9072	28908	11400	14976	14704	28116	9804	25920	11760

n	29421	29422	29423	29424	29425	29426	29427	29428	29429	29430
φ(n)	16776	14352	29422	9792	21200	14712	18432	12600	29428	7776

n	29431	29432	29433	29434	29435	29436	29437	29438	29439	29440
φ(n)	27864	13536	19620	14716	19488	8880	29436	14320	19620	11264

n	29441	29442	29443	29444	29445	29446	29447	29448	29449	29450
φ(n)	28884	8400	29442	13824	14400	14722	26760	9792	25200	10800

n	29451	29452	29453	29454	29455	29456	29457	29458	29459	29460
φ(n)	19632	14256	29452	9816	22848	12576	19620	12240	29040	7840

n	29461	29462	29463	29464	29465	29466	29467	29468	29469	29470
φ(n)	27712	14730	15840	14112	22960	9816	29016	14352	16560	10080

n	29471	29472	29473	29474	29475	29476	29477	29478	29479	29480
φ(n)	27192	9792	29472	14736	15600	14736	25260	9248	28720	10560

n	29481	29482	29483	29484	29485	29486	29487	29488	29489	29490
φ(n)	18960	14740	29482	7776	23584	14080	19656	13824	28656	7856

n	29491	29492	29493	29494	29495	29496	29497	29498	29499	29500
φ(n)	22920	14400	18816	14746	22144	9824	27216	12348	19664	11600

n	29501	29502	29503	29504	29505	29506	29507	29508	29509	29510
φ(n)	29500	8880	29160	14720	13440	14752	27936	9832	28204	10848

n	29511	29512	29513	29514	29515	29516	29517	29518	29519	29520
φ(n)	19656	11520	26820	9836	23608	14352	19676	14758	25296	7680

n	29521	29522	29523	29524	29525	29526	29527	29528	29529	29530
φ(n)	28912	14224	18144	13200	23600	7776	29526	14760	18432	11808

n	29531	29532	29533	29534	29535	29536	29537	29538	29539	29540
φ(n)	29530	9328	25308	14766	14240	13440	29536	9828	29160	10080

n	29541	29542	29543	29544	29545	29546	29547	29548	29549	29550
φ(n)	19152	14770	28560	9840	22320	12480	16632	14432	27264	7840

n	29551	29552	29553	29554	29555	29556	29557	29558	29559	29560
φ(n)	28504	14768	19700	12660	22528	9840	26860	14778	19256	11808

n	29561	29562	29563	29564	29565	29566	29567	29568	29569	29570
φ(n)	24480	9072	26496	13968	15552	14782	29566	7680	29568	11824

n	29571	29572	29573	29574	29575	29576	29577	29578	29579	29580
φ(n)	19712	14784	29572	9360	18720	14784	19716	14124	26880	7168

n	29581	29582	29583	29584	29585	29586	29587	29588	29589	29590
φ(n)	29580	12672	18576	14448	23040	9860	29586	13632	16896	10720

n	29591	29592	29593	29594	29595	29596	29597	29598	29599	29600
φ(n)	29232	9792	29200	14796	15776	12600	27840	9864	29598	11520

n	29601	29602	29603	29604	29605	29606	29607	29608	29609	29610
φ(n)	15840	13680	25368	9864	22800	14560	19320	14800	28560	6624

n	29611	29612	29613	29614	29615	29616	29617	29618	29619	29620
φ(n)	29610	13440	19740	12672	23688	9856	25380	14500	19728	11840

n	29621	29622	29623	29624	29625	29626	29627	29628	29629	29630
φ(n)	28044	9872	26920	12144	15600	14812	26208	9864	29628	11848

n	29631	29632	29633	29634	29635	29636	29637	29638	29639	29640
φ(n)	15744	14784	29632	8960	23704	14280	19008	12096	29256	6912

n	29641	29642	29643	29644	29645	29646	29647	29648	29649	29650
φ(n)	29640	14820	19200	14820	18480	9720	28336	13824	19764	11840

n	29651	29652	29653	29654	29655	29656	29657	29658	29659	29660
φ(n)	29304	8448	27360	14826	15792	13440	28980	9884	23976	11856

n	29661	29662	29663	29664	29665	29666	29667	29668	29669	29670
φ(n)	19772	14830	29662	9792	22272	11664	16800	14832	29668	7392

n	29671	29672	29673	29674	29675	29676	29677	29678	29679	29680
φ(n)	29670	14832	16848	14400	23720	9888	29116	12600	18240	9984

n	29681	29682	29683	29684	29685	29686	29687	29688	29689	29690
φ(n)	29172	9216	29682	14400	15824	14842	25440	9888	26980	11872

n	29691	29692	29693	29694	29695	29696	29697	29698	29699	29700
φ(n)	19788	13680	28380	8400	23752	14336	18720	14340	27936	7200

n	29701	29702	29703	29704	29705	29706	29707	29708	29709	29710
φ(n)	25452	14850	19800	14352	21888	9900	29160	12720	19800	11880

n	29711	29712	29713	29714	29715	29716	29717	29718	29719	29720
φ(n)	25920	9888	28980	14596	13536	12672	29716	9072	29344	11872

n	29721	29722	29723	29724	29725	29726	29727	29728	29729	29730
φ(n)	19812	11520	29722	9904	22400	14608	19764	14848	24480	7920

n	29731	29732	29733	29734	29735	29736	29737	29738	29739	29740
φ(n)	27432	14864	16640	14866	22464	8352	29380	14868	18920	11888

n	29741	29742	29743	29744	29745	29746	29747	29748	29749	29750
φ(n)	29740	9912	25452	12480	15840	14628	29400	9504	29260	9600

n	29751	29752	29753	29754	29755	29756	29757	29758	29759	29760
φ(n)	19320	14872	29752	9072	21600	14448	15552	14878	29758	7680

n	29761	29762	29763	29764	29765	29766	29767	29768	29769	29770
φ(n)	29760	14212	19836	12744	23808	8800	27744	14640	19844	10944

n	29771	29772	29773	29774	29775	29776	29777	29778	29779	29780
φ(n)	25512	9912	28188	14886	15840	14880	27060	8496	29376	11904

n	29781	29782	29783	29784	29785	29786	29787	29788	29789	29790
φ(n)	19836	14890	26208	9216	19008	14560	19856	13520	29788	7920

n	29791	29792	29793	29794	29795	29796	29797	29798	29799	29800
φ(n)	28830	12096	19860	14896	23200	9120	29356	14536	15120	11840

n	29801	29802	29803	29804	29805	29806	29807	29808	29809	29810
φ(n)	28032	9932	29802	14900	15888	12768	29040	9504	27504	10800

n	29811	29812	29813	29814	29815	29816	29817	29818	29819	29820
φ(n)	18792	14336	25548	9936	23232	14904	19872	14016	29818	6720

n	29821	29822	29823	29824	29825	29826	29827	29828	29829	29830
φ(n)	27100	12960	19880	14848	23840	9936	25560	14912	19440	11232

n	29831	29832	29833	29834	29835	29836	29837	29838	29839	29840
φ(n)	28512	8960	29832	12780	13824	14916	29836	9944	29224	11904

n	29841	29842	29843	29844	29845	29846	29847	29848	29849	29850
φ(n)	16464	14532	27120	9936	23184	14922	19896	11520	28260	7920

n	29851	29852	29853	29854	29855	29856	29857	29858	29859	29860
φ(n)	29850	14016	19080	12760	20448	9920	29376	14928	19296	11936

n	29861	29862	29863	29864	29865	29866	29867	29868	29869	29870
φ(n)	27552	8424	29862	14928	14400	14688	29866	9360	24000	11424

n	29871	29872	29873	29874	29875	29876	29877	29878	29879	29880
φ(n)	19908	14928	29872	9168	23800	11520	19008	14938	29878	7872

n	29881	29882	29883	29884	29885	29886	29887	29888	29889	29890
φ(n)	29880	14652	17064	14400	23184	9344	23760	14912	19440	10080

n	29891	29892	29893	29894	29895	29896	29897	29898	29899	29900
φ(n)	29400	9568	29548	14946	15936	14400	25620	9000	28840	10560

n	29901	29902	29903	29904	29905	29906	29907	29908	29909	29910
φ(n)	19932	14950	28128	8448	23920	14148	19932	14952	27180	7968

n	29911	29912	29913	29914	29915	29916	29917	29918	29919	29920
φ(n)	25632	14952	18096	14956	23040	9936	29916	12816	19944	10240

n	29921	29922	29923	29924	29925	29926	29927	29928	29929	29930
φ(n)	29920	9972	28600	14960	12960	13800	29926	9408	29756	11520

n	29931	29932	29933	29934	29935	29936	29937	29938	29939	29940
φ(n)	18120	12816	29088	9972	23944	14960	18752	14968	23184	7968

n	29941	29942	29943	29944	29945	29946	29947	29948	29949	29950
φ(n)	29484	13600	19944	14112	23296	7920	29946	14972	19536	11960

n	29951	29952	29953	29954	29955	29956	29957	29958	29959	29960
φ(n)	29400	9216	23280	14080	15968	14976	28896	9984	29958	10176

n	29961	29962	29963	29964	29965	29966	29967	29968	29969	29970
φ(n)	19968	14700	28044	9040	22080	14982	17112	14976	28644	7776

n	29971	29972	29973	29974	29975	29976	29977	29978	29979	29980
φ(n)	26880	14616	19584	12840	21600	9984	28980	13824	19980	11984

n	29981	29982	29983	29984	29985	29986	29987	29988	29989	29990
φ(n)	25692	9432	29982	14976	15984	12880	29640	8064	29988	11992

n	29991	29992	29993	29994	29995	29996	29997	29998	29999	30000
φ(n)	18432	14256	29568	9996	20544	14996	18000	14664	29640	8000

J.P. Martin-Flatin