]> Euler's Totient Function for n = 53001..54000

Euler's Totient Function for n = 53001..54000

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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	53001	53002	53003	53004	53005	53006	53007	53008	53009	53010
φ(n)	32400	26500	53002	15120	42400	24928	35336	26496	46800	12960

n	53011	53012	53013	53014	53015	53016	53017	53018	53019	53020
φ(n)	45432	25536	34400	24456	40480	17296	53016	22680	34272	19200

n	53021	53022	53023	53024	53025	53026	53027	53028	53029	53030
φ(n)	51552	17672	49888	26496	24000	26512	48936	17640	50220	21208

n	53031	53032	53033	53034	53035	53036	53037	53038	53039	53040
φ(n)	32120	22704	52560	17676	42424	26516	34440	25344	45456	12288

n	53041	53042	53043	53044	53045	53046	53047	53048	53049	53050
φ(n)	48720	24100	35360	26048	42024	15120	53046	25056	35364	21200

n	53051	53052	53053	53054	53055	53056	53057	53058	53059	53060
φ(n)	53050	17680	37440	25840	28080	26496	49920	17136	52416	18144

n	53061	53062	53063	53064	53065	53066	53067	53068	53069	53070
φ(n)	33792	25872	51888	15840	42448	24336	28728	26532	53068	13440

n	53071	53072	53073	53074	53075	53076	53077	53078	53079	53080
φ(n)	52272	25440	35376	21312	38400	17688	53076	26538	32640	21216

n	53081	53082	53083	53084	53085	53086	53087	53088	53089	53090
φ(n)	45492	17676	52488	25344	28304	22680	53086	14976	53088	21232

n	53091	53092	53093	53094	53095	53096	53097	53098	53099	53100
φ(n)	33216	24480	53092	17696	34560	26544	32160	26220	51240	13920

n	53101	53102	53103	53104	53105	53106	53107	53108	53109	53110
φ(n)	53100	22752	34200	26544	36288	17264	50776	22400	30240	20608

n	53111	53112	53113	53114	53115	53116	53117	53118	53119	53120
φ(n)	52632	17696	53112	26556	28320	22680	53116	16272	48180	20992

n	53121	53122	53123	53124	53125	53126	53127	53128	53129	53130
φ(n)	35412	26560	45528	16704	40000	26200	35412	25536	53128	10560

n	53131	53132	53133	53134	53135	53136	53137	53138	53139	53140
φ(n)	47520	25776	34848	25680	42504	17280	45540	26406	35424	21248

n	53141	53142	53143	53144	53145	53146	53147	53148	53149	53150
φ(n)	48300	16640	50328	20736	28320	26572	53146	17136	53148	21240

n	53151	53152	53153	53154	53155	53156	53157	53158	53159	53160
φ(n)	30360	24000	50820	17712	42520	26112	30912	22776	48256	14144

n	53161	53162	53163	53164	53165	53166	53167	53168	53169	53170
φ(n)	53160	25164	32040	26580	35280	17720	52416	26576	34416	19584

n	53171	53172	53173	53174	53175	53176	53177	53178	53179	53180
φ(n)	53170	15120	53172	24160	28320	23936	51840	17724	44520	21264

n	53181	53182	53183	53184	53185	53186	53187	53188	53189	53190
φ(n)	33480	26590	49080	17664	38640	21840	35456	26592	53188	14112

n	53191	53192	53193	53194	53195	53196	53197	53198	53199	53200
φ(n)	51912	25920	28416	26596	42552	14400	53196	26136	33792	17280

n	53201	53202	53203	53204	53205	53206	53207	53208	53209	53210
φ(n)	53200	17732	52480	25944	28368	25848	41400	17712	49104	19968

n	53211	53212	53213	53214	53215	53216	53217	53218	53219	53220
φ(n)	35472	26000	52668	15120	40992	26592	34992	23200	50400	14176

n	53221	53222	53223	53224	53225	53226	53227	53228	53229	53230
φ(n)	45612	23232	34944	26608	42560	17736	48000	22800	32240	21288

n	53231	53232	53233	53234	53235	53236	53237	53238	53239	53240
φ(n)	53230	17728	53232	25956	22464	26616	52716	16776	53238	19360

n	53241	53242	53243	53244	53245	53246	53247	53248	53249	53250
φ(n)	35492	22812	51768	16128	40656	26208	35496	24576	45636	14000

n	53251	53252	53253	53254	53255	53256	53257	53258	53259	53260
φ(n)	46920	26624	34560	26626	42600	15168	50436	25740	34560	21296

n	53261	53262	53263	53264	53265	53266	53267	53268	53269	53270
φ(n)	46080	16080	45612	26624	27456	26632	53266	16896	53268	18240

n	53271	53272	53273	53274	53275	53276	53277	53278	53279	53280
φ(n)	35496	26632	46480	16368	42600	25200	29232	25056	53278	13824

n	53281	53282	53283	53284	53285	53286	53287	53288	53289	53290
φ(n)	53280	26640	35520	20640	42624	17384	49176	26640	34200	21024

n	53291	53292	53293	53294	53295	53296	53297	53298	53299	53300
φ(n)	43560	17760	52768	26646	23040	26640	52836	14904	53298	19200

n	53301	53302	53303	53304	53305	53306	53307	53308	53309	53310
φ(n)	34992	25704	52800	17760	36528	24220	35532	26652	53308	14208

n	53311	53312	53313	53314	53315	53316	53317	53318	53319	53320
φ(n)	52624	21504	32784	23760	42648	17760	46800	26104	30456	20160

n	53321	53322	53323	53324	53325	53326	53327	53328	53329	53330
φ(n)	52500	17772	53322	26660	28080	21024	53326	16000	50176	21328

n	53331	53332	53333	53334	53335	53336	53337	53338	53339	53340
φ(n)	34272	26136	43200	17772	42664	25984	33968	26668	44640	12096

n	53341	53342	53343	53344	53345	53346	53347	53348	53349	53350
φ(n)	52000	26344	35556	26656	41584	16704	45720	26672	35564	19200

n	53351	53352	53353	53354	53355	53356	53357	53358	53359	53360
φ(n)	51600	15552	53352	22032	28448	26676	52896	17784	53358	19712

n	53361	53362	53363	53364	53365	53366	53367	53368	53369	53370
φ(n)	27720	26680	48384	17784	39360	26682	35576	22848	52644	14208

n	53371	53372	53373	53374	53375	53376	53377	53378	53379	53380
φ(n)	49608	24240	35580	26686	36000	17664	53376	24624	35532	19968

n	53381	53382	53383	53384	53385	53386	53387	53388	53389	53390
φ(n)	53380	14400	46200	26688	28464	26692	52920	17784	44016	20160

n	53391	53392	53393	53394	53395	53396	53397	53398	53399	53400
φ(n)	31968	25760	52788	16160	41760	22872	33408	26698	52536	14080

n	53401	53402	53403	53404	53405	53406	53407	53408	53409	53410
φ(n)	53400	26700	30504	24336	38800	16632	53406	26688	33696	18144

n	53411	53412	53413	53414	53415	53416	53417	53418	53419	53420
φ(n)	53410	17800	51660	25120	28464	24240	42192	17136	53418	21360

n	53421	53422	53423	53424	53425	53426	53427	53428	53429	53430
φ(n)	35612	26710	52080	14976	42720	26712	32360	24624	50600	13056

n	53431	53432	53433	53434	53435	53436	53437	53438	53439	53440
φ(n)	43008	26712	35604	26716	42744	17280	53436	20760	34776	21248

n	53441	53442	53443	53444	53445	53446	53447	53448	53449	53450
φ(n)	53440	17808	49320	25800	24384	26722	48384	16640	47040	21360

n	53451	53452	53453	53454	53455	53456	53457	53458	53459	53460
φ(n)	35628	21648	53452	17400	42760	24576	35088	26728	45780	12960

n	53461	53462	53463	53464	53465	53466	53467	53468	53469	53470
φ(n)	52992	26730	35000	25920	39168	14256	52920	26732	32832	21384

n	53471	53472	53473	53474	53475	53476	53477	53478	53479	53480
φ(n)	48600	17792	45828	26736	26400	25760	52416	17820	53478	18240

n	53481	53482	53483	53484	53485	53486	53487	53488	53489	53490
φ(n)	35652	21120	52728	17824	40464	26128	30456	26736	52800	14256

n	53491	53492	53493	53494	53495	53496	53497	53498	53499	53500
φ(n)	52984	26040	32400	22920	39456	17808	52560	25564	33536	21200

n	53501	53502	53503	53504	53505	53506	53507	53508	53509	53510
φ(n)	45852	17280	53502	23040	26880	25860	53506	14112	52704	21400

n	53511	53512	53513	53514	53515	53516	53517	53518	53519	53520
φ(n)	35672	26752	52548	17820	33120	25152	35676	26758	52920	14208

n	53521	53522	53523	53524	53525	53526	53527	53528	53529	53530
φ(n)	46992	22932	33696	26760	42800	16200	53526	26760	30576	20800

n	53531	53532	53533	53534	53535	53536	53537	53538	53539	53540
φ(n)	53064	17832	48576	23520	27552	22848	46800	17844	52056	21408

n	53541	53542	53543	53544	53545	53546	53547	53548	53549	53550
φ(n)	35640	25344	45888	16896	42832	26080	32928	24320	53548	11520

n	53551	53552	53553	53554	53555	53556	53557	53558	53559	53560
φ(n)	53550	26768	35700	26776	42840	17848	45864	26280	32400	19584

n	53561	53562	53563	53564	53565	53566	53567	53568	53569	53570
φ(n)	50724	17472	51688	22944	28560	26782	47872	17280	53568	19440

n	53571	53572	53573	53574	53575	53576	53577	53578	53579	53580
φ(n)	30600	26216	49296	17856	42840	25920	35712	22176	53040	13248

n	53581	53582	53583	53584	53585	53586	53587	53588	53589	53590
φ(n)	48700	26352	34944	25088	36720	16416	52240	26792	35724	20416

n	53591	53592	53593	53594	53595	53596	53597	53598	53599	53600
φ(n)	53590	13440	53592	26460	28512	26796	53596	17864	38880	21120

n	53601	53602	53603	53604	53605	53606	53607	53608	53609	53610
φ(n)	33600	26800	48620	17856	42000	22932	35192	26800	53608	14288

n	53611	53612	53613	53614	53615	53616	53617	53618	53619	53620
φ(n)	53610	24720	28512	24360	42888	17856	53616	23616	35040	18336

n	53621	53622	53623	53624	53625	53626	53627	53628	53629	53630
φ(n)	50568	17820	53622	26808	24000	26812	44712	17280	53628	20640

n	53631	53632	53633	53634	53635	53636	53637	53638	53639	53640
φ(n)	34800	26752	53632	15312	40320	22880	33840	24744	53638	14208

n	53641	53642	53643	53644	53645	53646	53647	53648	53649	53650
φ(n)	44928	26820	35760	26820	42912	17880	48760	22944	35748	20160

n	53651	53652	53653	53654	53655	53656	53657	53658	53659	53660
φ(n)	49512	16768	53652	26496	24192	25344	53656	16200	51304	21456

n	53661	53662	53663	53664	53665	53666	53667	53668	53669	53670
φ(n)	34560	22992	53040	16128	42928	26832	34848	26832	38400	14304

n	53671	53672	53673	53674	53675	53676	53677	53678	53679	53680
φ(n)	53200	26832	35780	26220	40320	15120	49536	26838	34496	19200

n	53681	53682	53683	53684	53685	53686	53687	53688	53689	53690
φ(n)	53680	17072	46008	26840	28608	25248	52200	17888	52624	16704

n	53691	53692	53693	53694	53695	53696	53697	53698	53699	53700
φ(n)	32520	25920	53692	16848	42952	26816	30672	26848	53698	14240

n	53701	53702	53703	53704	53705	53706	53707	53708	53709	53710
φ(n)	52972	24400	31104	22848	41008	17900	52416	25872	35804	20800

n	53711	53712	53713	53714	53715	53716	53717	53718	53719	53720
φ(n)	46032	17856	46080	26500	28640	24768	53716	15336	53718	19968

n	53721	53722	53723	53724	53725	53726	53727	53728	53729	53730
φ(n)	34776	26860	51960	15840	36720	26862	35816	25344	49584	14256

n	53731	53732	53733	53734	53735	53736	53737	53738	53739	53740
φ(n)	53730	21600	35820	26400	39040	17904	48384	26496	30672	21488

n	53741	53742	53743	53744	53745	53746	53747	53748	53749	53750
φ(n)	52800	16224	53280	26864	28656	20880	52920	17904	52780	21000

n	53751	53752	53753	53754	53755	53756	53757	53758	53759	53760
φ(n)	31680	26872	46032	16320	39648	26400	32400	26878	53758	12288

n	53761	53762	53763	53764	53765	53766	53767	53768	53769	53770
φ(n)	52272	26880	35840	26880	43008	17136	46080	22080	35844	20304

n	53771	53772	53773	53774	53775	53776	53777	53778	53779	53780
φ(n)	50592	17920	53772	21912	28560	26880	53776	17924	48880	21504

n	53781	53782	53783	53784	53785	53786	53787	53788	53789	53790
φ(n)	28224	26890	53782	17712	41520	26892	35856	21504	50616	12960

n	53791	53792	53793	53794	53795	53796	53797	53798	53799	53800
φ(n)	53790	26240	34776	24816	34944	17928	51436	26136	35256	21440

n	53801	53802	53803	53804	53805	53806	53807	53808	53809	53810
φ(n)	47520	15120	53320	26900	26880	26902	49656	16704	46116	21520

n	53811	53812	53813	53814	53815	53816	53817	53818	53819	53820
φ(n)	35856	24440	53812	17936	41952	22320	35876	26460	53818	12672

n	53821	53822	53823	53824	53825	53826	53827	53828	53829	53830
φ(n)	53212	25312	27840	25984	43040	17940	50976	26912	35880	18432

n	53831	53832	53833	53834	53835	53836	53837	53838	53839	53840
φ(n)	53830	17936	48000	24460	27648	26208	46140	17928	50656	21504

n	53841	53842	53843	53844	53845	53846	53847	53848	53849	53850
φ(n)	35360	26920	51480	15360	38720	23328	34560	26208	53848	14320

n	53851	53852	53853	53854	53855	53856	53857	53858	53859	53860
φ(n)	45864	26924	34608	26926	43080	15360	53856	23076	33120	21536

n	53861	53862	53863	53864	53865	53866	53867	53868	53869	53870
φ(n)	53860	17480	52920	26928	23328	25740	47560	17688	53244	21544

n	53871	53872	53873	53874	53875	53876	53877	53878	53879	53880
φ(n)	35912	20736	50688	17280	43000	26936	35916	23400	44856	14336

n	53881	53882	53883	53884	53885	53886	53887	53888	53889	53890
φ(n)	53880	25984	35916	25488	39744	15384	53886	26880	30800	20224

n	53891	53892	53893	53894	53895	53896	53897	53898	53899	53900
φ(n)	53890	17928	46188	26946	28736	26944	53896	16560	53898	16800

n	53901	53902	53903	53904	53905	53906	53907	53908	53909	53910
φ(n)	34944	26950	51048	17952	43120	26952	28800	26952	49680	14352

n	53911	53912	53913	53914	53915	53916	53917	53918	53919	53920
φ(n)	43680	25696	35940	23100	41920	17968	53916	26958	35928	21504

n	53921	53922	53923	53924	53925	53926	53927	53928	53929	53930
φ(n)	46212	15120	53922	23040	28720	26448	53926	15264	53460	21568

n	53931	53932	53933	53934	53935	53936	53937	53938	53939	53940
φ(n)	35952	26496	49020	17600	34848	26960	33120	26640	53938	13440

n	53941	53942	53943	53944	53945	53946	53947	53948	53949	53950
φ(n)	47808	23112	35960	24480	43152	17496	53136	26972	30744	19680

n	53951	53952	53953	53954	53955	53956	53957	53958	53959	53960
φ(n)	53950	17920	53460	26416	25920	22080	53196	16192	53958	20160

n	53961	53962	53963	53964	53965	53966	53967	53968	53969	53970
φ(n)	35972	26980	42624	17976	42000	24420	35976	26976	52080	12288

n	53971	53972	53973	53974	53975	53976	53977	53978	53979	53980
φ(n)	52200	26520	35964	26986	40320	16512	42000	26656	34056	21584

n	53981	53982	53983	53984	53985	53986	53987	53988	53989	53990
φ(n)	51612	17988	52488	23040	27840	26992	53986	16320	49824	21592

n	53991	53992	53993	53994	53995	53996	53997	53998	53999	54000
φ(n)	30816	25344	53992	17996	43192	26996	35040	21168	49080	14400

J.P. Martin-Flatin