]> Euler's Totient Function for n = 28001..29000

Euler's Totient Function for n = 28001..29000

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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	28001	28002	28003	28004	28005	28006	28007	28008	28009	28010
φ(n)	28000	8592	27280	14000	14928	11880	24000	9312	27216	11200

n	28011	28012	28013	28014	28015	28016	28017	28018	28019	28020
φ(n)	18672	13616	27648	7392	20640	13056	16920	14008	28018	7456

n	28021	28022	28023	28024	28025	28026	28027	28028	28029	28030
φ(n)	24012	14010	18680	13440	20880	9288	28026	10080	18684	11208

n	28031	28032	28033	28034	28035	28036	28037	28038	28039	28040
φ(n)	28030	9216	26112	13780	12672	13608	26312	9344	25480	11200

n	28041	28042	28043	28044	28045	28046	28047	28048	28049	28050
φ(n)	17232	12012	27048	8640	21840	13608	18696	14016	24036	6400

n	28051	28052	28053	28054	28055	28056	28057	28058	28059	28060
φ(n)	28050	14024	18684	12792	21600	7968	28056	14028	18216	10560

n	28061	28062	28063	28064	28065	28066	28067	28068	28069	28070
φ(n)	25500	9348	22680	14016	14960	14032	24192	9352	28068	9600

n	28071	28072	28073	28074	28075	28076	28077	28078	28079	28080
φ(n)	18708	12320	27588	9356	22440	14036	15960	13800	27384	6912

n	28081	28082	28083	28084	28085	28086	28087	28088	28089	28090
φ(n)	28080	13284	15840	11136	21760	9000	28086	14040	18720	11024

n	28091	28092	28093	28094	28095	28096	28097	28098	28099	28100
φ(n)	24072	9360	25920	12760	14976	14016	28096	7992	28098	11200

n	28101	28102	28103	28104	28105	28106	28107	28108	28109	28110
φ(n)	16128	14050	27768	9360	17280	12144	18684	14052	28108	7488

n	28111	28112	28113	28114	28115	28116	28117	28118	28119	28120
φ(n)	28110	12000	18740	14056	22488	8400	27180	13216	14688	10368

n	28121	28122	28123	28124	28125	28126	28127	28128	28129	28130
φ(n)	27600	9072	28122	13728	15000	11760	25560	9344	26884	10752

n	28131	28132	28133	28134	28135	28136	28137	28138	28139	28140
φ(n)	18752	12960	24108	9360	21120	14064	18368	12780	26640	6336

n	28141	28142	28143	28144	28145	28146	28147	28148	28149	28150
φ(n)	27772	14070	18096	14064	20736	9380	24120	13560	17040	11240

n	28151	28152	28153	28154	28155	28156	28157	28158	28159	28160
φ(n)	28150	8448	27508	12060	15008	14076	27360	8208	27160	10240

n	28161	28162	28163	28164	28165	28166	28167	28168	28169	28170
φ(n)	15984	14080	28162	9384	21840	14082	18240	12048	26496	7488

n	28171	28172	28173	28174	28175	28176	28177	28178	28179	28180
φ(n)	23520	14084	18780	14086	18480	9376	26676	13824	18000	11264

n	28181	28182	28183	28184	28185	28186	28187	28188	28189	28190
φ(n)	28180	7200	28182	12960	15024	13248	27720	9072	24156	11272

n	28191	28192	28193	28194	28195	28196	28197	28198	28199	28200
φ(n)	18792	14080	25520	9072	22552	11232	17280	13464	27864	7360

n	28201	28202	28203	28204	28205	28206	28207	28208	28209	28210
φ(n)	28200	13804	14976	12800	22560	9396	27720	13440	18804	8640

n	28211	28212	28213	28214	28215	28216	28217	28218	28219	28220
φ(n)	28210	9400	27808	14106	12960	14104	23184	9404	28218	10496

n	28221	28222	28223	28224	28225	28226	28227	28228	28229	28230
φ(n)	17952	13872	25896	8064	22560	12820	18624	14112	28228	7520

n	28231	28232	28233	28234	28235	28236	28237	28238	28239	28240
φ(n)	23328	14112	18816	13356	22584	8640	24000	12096	18824	11264

n	28241	28242	28243	28244	28245	28246	28247	28248	28249	28250
φ(n)	27300	9396	27720	13464	12864	13608	27600	8480	24960	11200

n	28251	28252	28253	28254	28255	28256	28257	28258	28259	28260
φ(n)	18144	12096	26748	8832	22600	14112	18836	13860	21960	7488

n	28261	28262	28263	28264	28265	28266	28267	28268	28269	28270
φ(n)	27724	13032	18840	14128	22608	8064	27016	13680	18792	10240

n	28271	28272	28273	28274	28275	28276	28277	28278	28279	28280
φ(n)	26592	8640	24192	13860	13440	14136	28276	9420	28278	9600

n	28281	28282	28283	28284	28285	28286	28287	28288	28289	28290
φ(n)	17120	13884	28282	9424	22624	14142	16128	12288	28288	7040

n	28291	28292	28293	28294	28295	28296	28297	28298	28299	28300
φ(n)	26784	12840	18860	11592	22632	9360	28296	14148	18864	11280

n	28301	28302	28303	28304	28305	28306	28307	28308	28309	28310
φ(n)	22320	9152	24600	13440	13824	14152	28306	8064	28308	10656

n	28311	28312	28313	28314	28315	28316	28317	28318	28319	28320
φ(n)	18872	14152	27060	7920	19392	14156	18876	14158	28318	7424

n	28321	28322	28323	28324	28325	28326	28327	28328	28329	28330
φ(n)	27972	11424	18864	13824	20400	9440	26136	14160	15120	11328

n	28331	28332	28333	28334	28335	28336	28337	28338	28339	28340
φ(n)	27600	9432	27328	13680	15104	10560	27636	9444	26656	10368

n	28341	28342	28343	28344	28345	28346	28347	28348	28349	28350
φ(n)	18216	13752	24288	9440	22672	14172	17160	13392	28348	6480

n	28351	28352	28353	28354	28355	28356	28357	28358	28359	28360
φ(n)	28350	14144	17424	14176	22048	8832	24300	12880	17952	11328

n	28361	28362	28363	28364	28365	28366	28367	28368	28369	28370
φ(n)	27924	9072	28000	12144	14400	13080	26856	9408	25780	11344

n	28371	28372	28373	28374	28375	28376	28377	28378	28379	28380
φ(n)	16128	13760	26688	9456	22600	14184	18900	12156	25056	6720

n	28381	28382	28383	28384	28385	28386	28387	28388	28389	28390
φ(n)	28000	13552	18920	14176	19440	8856	28386	13800	18924	10624

n	28391	28392	28393	28394	28395	28396	28397	28398	28399	28400
φ(n)	24640	7488	28392	14196	15120	13680	27936	9464	24336	11200

n	28401	28402	28403	28404	28405	28406	28407	28408	28409	28410
φ(n)	18932	12900	28402	9432	19008	12168	17792	13728	28408	7568

n	28411	28412	28413	28414	28415	28416	28417	28418	28419	28420
φ(n)	28410	14204	14400	14206	22728	9216	28080	13104	18944	9408

n	28421	28422	28423	28424	28425	28426	28427	28428	28429	28430
φ(n)	28032	9468	27720	11520	15120	13920	23400	8976	28428	11368

n	28431	28432	28433	28434	28435	28436	28437	28438	28439	28440
φ(n)	17496	14208	28432	8112	20240	14216	18956	13920	28438	7488

n	28441	28442	28443	28444	28445	28446	28447	28448	28449	28450
φ(n)	22848	14220	17928	13104	22752	8600	28446	12096	18144	11360

n	28451	28452	28453	28454	28455	28456	28457	28458	28459	28460
φ(n)	27192	9480	27648	13840	12960	14224	23760	8640	28120	11376

n	28461	28462	28463	28464	28465	28466	28467	28468	28469	28470
φ(n)	18512	11448	28462	9472	22768	13860	18972	12920	24108	6912

n	28471	28472	28473	28474	28475	28476	28477	28478	28479	28480
φ(n)	28000	14232	18980	13596	21120	8064	28476	13720	17240	11264

n	28481	28482	28483	28484	28485	28486	28487	28488	28489	28490
φ(n)	26964	9200	22464	14240	15120	14242	27960	9488	27540	8640

n	28491	28492	28493	28494	28495	28496	28497	28498	28499	28500
φ(n)	18992	13376	28492	9492	22080	13056	15312	14248	28498	7200

n	28501	28502	28503	28504	28505	28506	28507	28508	28509	28510
φ(n)	25900	14250	18996	12192	22800	9500	27496	14252	16128	11400

n	28511	28512	28513	28514	28515	28516	28517	28518	28519	28520
φ(n)	24432	8640	28512	13936	15200	14256	28516	8064	26676	10560

n	28521	28522	28523	28524	28525	28526	28527	28528	28529	28530
φ(n)	19008	13152	25920	9504	19440	13408	18432	14256	27876	7584

n	28531	28532	28533	28534	28535	28536	28537	28538	28539	28540
φ(n)	28152	12216	19020	12960	21024	8960	28536	13500	16200	11408

n	28541	28542	28543	28544	28545	28546	28547	28548	28549	28550
φ(n)	28540	9240	25344	14208	13760	12228	28546	8640	28548	11400

n	28551	28552	28553	28554	28555	28556	28557	28558	28559	28560
φ(n)	18360	13776	24468	9516	22840	12760	17928	14040	28558	6144

n	28561	28562	28563	28564	28565	28566	28567	28568	28569	28570
φ(n)	26364	14280	19040	13824	21952	9108	21840	14280	18656	11424

n	28571	28572	28573	28574	28575	28576	28577	28578	28579	28580
φ(n)	28570	9520	28572	11232	15120	13248	26240	8640	28578	11424

n	28581	28582	28583	28584	28585	28586	28587	28588	28589	28590
φ(n)	16320	13800	28200	9504	22864	14292	17568	12240	24640	7616

n	28591	28592	28593	28594	28595	28596	28597	28598	28599	28600
φ(n)	28590	14288	19008	12992	18144	9528	28596	14040	19064	9600

n	28601	28602	28603	28604	28605	28606	28607	28608	28609	28610
φ(n)	27792	8136	28602	14300	15248	14302	28606	9472	23760	11440

n	28611	28612	28613	28614	28615	28616	28617	28618	28619	28620
φ(n)	16320	13640	25200	9000	22272	12096	19076	13920	28618	7488

n	28621	28622	28623	28624	28625	28626	28627	28628	28629	28630
φ(n)	28620	13000	15456	14304	22800	8784	28626	13440	19080	9792

n	28631	28632	28633	28634	28635	28636	28637	28638	28639	28640
φ(n)	28630	9536	24480	14076	14432	14316	24540	9072	26424	11392

n	28641	28642	28643	28644	28645	28646	28647	28648	28649	28650
φ(n)	19092	14320	28642	7200	21504	14322	19080	14320	28648	7600

n	28651	28652	28653	28654	28655	28656	28657	28658	28659	28660
φ(n)	24552	12096	19100	14326	20800	9504	28656	11616	18560	11456

n	28661	28662	28663	28664	28665	28666	28667	28668	28669	28670
φ(n)	28660	8960	28662	14328	12096	13020	28296	9552	28668	11040

n	28671	28672	28673	28674	28675	28676	28677	28678	28679	28680
φ(n)	18072	12288	28080	9396	21600	13992	17160	13224	23040	7616

n	28681	28682	28683	28684	28685	28686	28687	28688	28689	28690
φ(n)	25872	14340	19116	14000	22944	8184	28686	12960	18720	10800

n	28691	28692	28693	28694	28695	28696	28697	28698	28699	28700
φ(n)	26472	9552	24588	14346	15296	13440	28696	9564	26080	9600

n	28701	28702	28703	28704	28705	28706	28707	28708	28709	28710
φ(n)	19116	14112	28702	8448	22960	13860	16392	14352	27180	6720

n	28711	28712	28713	28714	28715	28716	28717	28718	28719	28720
φ(n)	28710	13824	17984	12264	22968	9568	25944	14104	19140	11456

n	28721	28722	28723	28724	28725	28726	28727	28728	28729	28730
φ(n)	22320	9572	28722	13944	15280	14040	27456	7776	28728	9984

n	28731	28732	28733	28734	28735	28736	28737	28738	28739	28740
φ(n)	18720	13040	28188	9576	19680	14336	18360	14368	27720	7648

n	28741	28742	28743	28744	28745	28746	28747	28748	28749	28750
φ(n)	28000	12312	15840	14368	22992	9576	25344	14372	15984	11000

n	28751	28752	28753	28754	28755	28756	28757	28758	28759	28760
φ(n)	28750	9568	28752	13060	15120	11232	28416	9584	28758	11488

n	28761	28762	28763	28764	28765	28766	28767	28768	28769	28770
φ(n)	19172	14112	24612	8832	20880	13608	18648	13440	26544	6528

n	28771	28772	28773	28774	28775	28776	28777	28778	28779	28780
φ(n)	28770	14384	18216	14386	23000	8640	24660	14388	18720	11504

n	28781	28782	28783	28784	28785	28786	28787	28788	28789	28790
φ(n)	27072	8640	28408	12288	14400	13968	26160	9592	28788	11512

n	28791	28792	28793	28794	28795	28796	28797	28798	28799	28800
φ(n)	16416	13920	28792	9596	21216	13728	18480	10560	27840	7680

n	28801	28802	28803	28804	28805	28806	28807	28808	28809	28810
φ(n)	28372	14400	19200	13608	19728	9600	28806	13248	17280	11088

n	28811	28812	28813	28814	28815	28816	28817	28818	28819	28820
φ(n)	28152	8232	28812	14406	14336	14400	28816	9600	23496	10400

n	28821	28822	28823	28824	28825	28826	28827	28828	28829	28830
φ(n)	17712	14410	25920	9600	23040	11760	19212	14412	28476	7440

n	28831	28832	28833	28834	28835	28836	28837	28838	28839	28840
φ(n)	26200	13312	16464	13296	22464	9504	28836	14418	19224	9792

n	28841	28842	28843	28844	28845	28846	28847	28848	28849	28850
φ(n)	28500	7920	28842	14420	15360	14422	22752	9600	27136	11520

n	28851	28852	28853	28854	28855	28856	28857	28858	28859	28860
φ(n)	18792	14424	25200	8208	22176	14424	19236	14076	28858	6912

n	28861	28862	28863	28864	28865	28866	28867	28868	28869	28870
φ(n)	22680	14430	19224	12800	22000	9024	28866	12360	19244	11544

n	28871	28872	28873	28874	28875	28876	28877	28878	28879	28880
φ(n)	28870	9600	26640	14436	12000	14436	28380	9624	28878	10944

n	28881	28882	28883	28884	28885	28886	28887	28888	28889	28890
φ(n)	19248	12372	27168	9184	22464	12000	19256	13728	24756	7632

n	28891	28892	28893	28894	28895	28896	28897	28898	28899	28900
φ(n)	28552	13920	19260	14446	23112	8064	25200	14448	16848	10880

n	28901	28902	28903	28904	28905	28906	28907	28908	28909	28910
φ(n)	28900	9632	24768	14448	14720	14208	28560	8640	28908	9744

n	28911	28912	28913	28914	28915	28916	28917	28918	28919	28920
φ(n)	18392	13248	27888	9360	23128	14456	15552	13680	26180	7680

n	28921	28922	28923	28924	28925	28926	28927	28928	28929	28930
φ(n)	28920	14460	18600	12384	21120	9636	28926	14336	19284	10480

n	28931	28932	28933	28934	28935	28936	28937	28938	28939	28940
φ(n)	24792	9640	28932	12672	15408	14464	27396	7488	28224	11568

n	28941	28942	28943	28944	28945	28946	28947	28948	28949	28950
φ(n)	17520	13944	28560	9504	19824	14080	19296	14472	28948	7680

n	28951	28952	28953	28954	28955	28956	28957	28958	28959	28960
φ(n)	24960	11040	19296	13980	23160	9072	27676	14478	16464	11520

n	28961	28962	28963	28964	28965	28966	28967	28968	28969	28970
φ(n)	28960	9648	26320	13344	15440	12408	28536	8960	28420	11584

n	28971	28972	28973	28974	28975	28976	28977	28978	28979	28980
φ(n)	18144	14484	24828	8760	21600	14480	17808	14488	28978	6336

n	28981	28982	28983	28984	28985	28986	28987	28988	28989	28990
φ(n)	28512	14112	19320	14488	19200	9660	24000	14492	19320	10656

n	28991	28992	28993	28994	28995	28996	28997	28998	28999	29000
φ(n)	28392	9600	28548	11664	15456	13160	28620	9612	28336	11200

J.P. Martin-Flatin