]> Euler's Totient Function for n = 19001..20000

Euler's Totient Function for n = 19001..20000

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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	19001	19002	19003	19004	19005	19006	19007	19008	19009	19010
φ(n)	19000	6332	18360	9500	8640	8064	18696	5760	19008	7600

n	19011	19012	19013	19014	19015	19016	19017	19018	19019	19020
φ(n)	12672	8064	19012	6336	15208	9504	12672	9216	12960	5056

n	19021	19022	19023	19024	19025	19026	19027	19028	19029	19030
φ(n)	18172	9510	11904	8960	15200	5400	18616	9240	12684	6880

n	19031	19032	19033	19034	19035	19036	19037	19038	19039	19040
φ(n)	19030	5760	16308	9180	9936	9516	19036	5976	18720	6144

n	19041	19042	19043	19044	19045	19046	19047	19048	19049	19050
φ(n)	11520	9520	18768	6072	14016	9328	10872	9520	18564	5040

n	19051	19052	19053	19054	19055	19056	19057	19058	19059	19060
φ(n)	19050	8640	12096	8160	14688	6336	16704	8784	12704	7616

n	19061	19062	19063	19064	19065	19066	19067	19068	19069	19070
φ(n)	16296	6336	17320	9528	9600	9532	18216	5424	19068	7624

n	19071	19072	19073	19074	19075	19076	19077	19078	19079	19080
φ(n)	11664	9472	19072	5440	12960	9000	12716	9538	19078	4992

n	19081	19082	19083	19084	19085	19086	19087	19088	19089	19090
φ(n)	19080	7728	12720	8784	13840	6360	19086	9536	10800	7216

n	19091	19092	19093	19094	19095	19096	19097	19098	19099	19100
φ(n)	17952	6048	18720	9546	9504	7200	17472	6360	18760	7600

n	19101	19102	19103	19104	19105	19106	19107	19108	19109	19110
φ(n)	12732	9550	16368	6336	15280	9280	11520	8960	18816	4032

n	19111	19112	19113	19114	19115	19116	19117	19118	19119	19120
φ(n)	18424	9552	12144	9036	15288	6264	16380	8580	12744	7616

n	19121	19122	19123	19124	19125	19126	19127	19128	19129	19130
φ(n)	19120	6372	17640	8184	9600	9360	18480	6368	16560	7648

n	19131	19132	19133	19134	19135	19136	19137	19138	19139	19140
φ(n)	10920	9564	17784	6372	14784	8448	12756	8196	19138	4480

n	19141	19142	19143	19144	19145	19146	19147	19148	19149	19150
φ(n)	19140	8992	12744	9568	13104	6380	18640	9572	11760	7640

n	19151	19152	19153	19154	19155	19156	19157	19158	19159	19160
φ(n)	17400	5184	18868	9360	10208	9576	19156	6120	14784	7648

n	19161	19162	19163	19164	19165	19166	19167	19168	19169	19170
φ(n)	12768	7920	19162	6384	15328	7992	12776	9568	18480	5040

n	19171	19172	19173	19174	19175	19176	19177	19178	19179	19180
φ(n)	18144	9584	9840	9586	13920	5888	18900	9324	12780	6528

n	19181	19182	19183	19184	19185	19186	19187	19188	19189	19190
φ(n)	19180	6072	19182	8640	10224	9360	16440	5760	18540	7200

n	19191	19192	19193	19194	19195	19196	19197	19198	19199	19200
φ(n)	12792	9592	18048	5472	13920	9596	12636	9240	18864	5120

n	19201	19202	19203	19204	19205	19206	19207	19208	19209	19210
φ(n)	15120	9600	12384	9600	14608	5760	19206	8232	12096	7168

n	19211	19212	19213	19214	19215	19216	19217	19218	19219	19220
φ(n)	19210	6400	19212	8856	8640	9600	17460	6404	19218	7440

n	19221	19222	19223	19224	19225	19226	19227	19228	19229	19230
φ(n)	12432	8232	18768	6336	15360	9612	10752	7920	15840	5120

n	19231	19232	19233	19234	19235	19236	19237	19238	19239	19240
φ(n)	19230	9600	12816	9396	15384	5472	19236	9618	11440	6912

n	19241	19242	19243	19244	19245	19246	19247	19248	19249	19250
φ(n)	18900	6408	16488	9024	10256	9622	18216	6400	19248	6000

n	19251	19252	19253	19254	19255	19256	19257	19258	19259	19260
φ(n)	11880	9624	17760	6416	15400	9184	10920	9628	19258	5088

n	19261	19262	19263	19264	19265	19266	19267	19268	19269	19270
φ(n)	16320	9630	12840	8064	15408	5616	19266	9632	12840	7360

n	19271	19272	19273	19274	19275	19276	19277	19278	19279	19280
φ(n)	16512	5760	19272	9196	10240	9360	18720	5184	17784	7680

n	19281	19282	19283	19284	19285	19286	19287	19288	19289	19290
φ(n)	12852	9300	17520	6424	12096	9642	12852	9640	19288	5136

n	19291	19292	19293	19294	19295	19296	19297	19298	19299	19300
φ(n)	19000	7488	12528	8760	14464	6336	18436	9648	11016	7680

n	19301	19302	19303	19304	19305	19306	19307	19308	19309	19310
φ(n)	19300	6432	19008	9072	8640	8232	18816	6432	19308	7720

n	19311	19312	19313	19314	19315	19316	19317	19318	19319	19320
φ(n)	12480	8960	15840	6048	15448	8760	12512	8904	19318	4224

n	19321	19322	19323	19324	19325	19326	19327	19328	19329	19330
φ(n)	19182	9660	12096	9660	15440	6440	15000	9600	12096	7728

n	19331	19332	19333	19334	19335	19336	19337	19338	19339	19340
φ(n)	17832	6408	19332	8280	10304	9664	18960	5840	19024	7728

n	19341	19342	19343	19344	19345	19346	19347	19348	19349	19350
φ(n)	11016	9144	17864	5760	14976	9088	12896	8280	17580	5040

n	19351	19352	19353	19354	19355	19356	19357	19358	19359	19360
φ(n)	18792	9280	12900	9676	13104	6448	17856	9678	12852	7040

n	19361	19362	19363	19364	19365	19366	19367	19368	19369	19370
φ(n)	18324	5520	17952	9384	10320	9240	19080	6432	16596	7104

n	19371	19372	19373	19374	19375	19376	19377	19378	19379	19380
φ(n)	11720	9296	19372	6456	15000	8256	12912	9688	19378	4608

n	19381	19382	19383	19384	19385	19386	19387	19388	19389	19390
φ(n)	19380	8800	10080	9688	15504	6444	19386	9360	12320	6624

n	19391	19392	19393	19394	19395	19396	19397	19398	19399	19400
φ(n)	19390	6400	16800	9696	10320	8928	15552	6240	18360	7680

n	19401	19402	19403	19404	19405	19406	19407	19408	19409	19410
φ(n)	12432	9504	19402	5040	15520	9360	12936	9696	17904	5168

n	19411	19412	19413	19414	19415	19416	19417	19418	19419	19420
φ(n)	16008	9240	12924	9120	14080	6464	19416	7776	12944	7760

n	19421	19422	19423	19424	19425	19426	19427	19428	19429	19430
φ(n)	19420	5904	19422	9696	8640	8820	19426	6472	19428	7392

n	19431	19432	19433	19434	19435	19436	19437	19438	19439	19440
φ(n)	12096	8304	19432	6240	13728	9408	10800	9718	16656	5184

n	19441	19442	19443	19444	19445	19446	19447	19448	19449	19450
φ(n)	19440	9720	12960	9720	15552	5544	19446	7680	12960	7760

n	19451	19452	19453	19454	19455	19456	19457	19458	19459	19460
φ(n)	19032	6480	16632	9520	10368	9216	19456	6072	16800	6624

n	19461	19462	19463	19464	19465	19466	19467	19468	19469	19470
φ(n)	11952	9432	19462	6480	14592	9732	11016	9360	19468	4640

n	19471	19472	19473	19474	19475	19476	19477	19478	19479	19480
φ(n)	19470	9728	12980	7632	14400	6480	19476	9738	12600	7776

n	19481	19482	19483	19484	19485	19486	19487	19488	19489	19490
φ(n)	14520	6080	19482	9740	10368	9742	17976	5376	19488	7792

n	19491	19492	19493	19494	19495	19496	19497	19498	19499	19500
φ(n)	12672	8840	19200	6156	13344	9744	12672	9748	17280	4800

n	19501	19502	19503	19504	19505	19506	19507	19508	19509	19510
φ(n)	19500	8316	11760	9152	15088	6500	19506	9752	11136	7800

n	19511	19512	19513	19514	19515	19516	19517	19518	19519	19520
φ(n)	19224	6480	16848	8860	10400	7680	18816	6504	19240	7680

n	19521	19522	19523	19524	19525	19526	19527	19528	19529	19530
φ(n)	12960	9492	16728	6504	14000	9000	12408	9760	19140	4320

n	19531	19532	19533	19534	19535	19536	19537	19538	19539	19540
φ(n)	19530	9216	12224	9766	15624	5760	16740	9768	11952	7808

n	19541	19542	19543	19544	19545	19546	19547	19548	19549	19550
φ(n)	19540	6512	19542	8352	10416	9408	17760	6480	19264	7040

n	19551	19552	19553	19554	19555	19556	19557	19558	19559	19560
φ(n)	10584	8832	19552	6516	15640	9776	12480	7560	19558	5184

n	19561	19562	19563	19564	19565	19566	19567	19568	19569	19570
φ(n)	18900	9780	13040	9504	12096	6516	18400	9776	11840	7344

n	19571	19572	19573	19574	19575	19576	19577	19578	19579	19580
φ(n)	19570	5568	18216	9786	10080	9784	19576	6000	16776	7040

n	19581	19582	19583	19584	19585	19586	19587	19588	19589	19590
φ(n)	12720	9790	19582	6144	15664	8388	13056	9512	18540	5216

n	19591	19592	19593	19594	19595	19596	19597	19598	19599	19600
φ(n)	16320	9360	11160	9600	15672	6160	19596	9520	12696	6720

n	19601	19602	19603	19604	19605	19606	19607	19608	19609	19610
φ(n)	18432	5940	19602	8736	10448	9802	16800	6048	19608	7488

n	19611	19612	19613	19614	19615	19616	19617	19618	19619	19620
φ(n)	13068	9804	17820	5592	15688	9792	12048	9216	18744	5184

n	19621	19622	19623	19624	19625	19626	19627	19628	19629	19630
φ(n)	16812	9810	12600	8880	15600	6540	18576	8400	13068	7200

n	19631	19632	19633	19634	19635	19636	19637	19638	19639	19640
φ(n)	19272	6528	18928	9816	7680	9816	19296	6540	19120	7840

n	19641	19642	19643	19644	19645	19646	19647	19648	19649	19650
φ(n)	13092	7920	18120	6544	15712	8280	12528	9792	16800	5200

n	19651	19652	19653	19654	19655	19656	19657	19658	19659	19660
φ(n)	19152	9248	13100	9480	15720	5184	17860	9828	13104	7856

n	19661	19662	19663	19664	19665	19666	19667	19668	19669	19670
φ(n)	19660	6272	16536	9824	9504	9832	19320	5920	16896	6720

n	19671	19672	19673	19674	19675	19676	19677	19678	19679	19680
φ(n)	12792	9832	19380	6552	15720	9836	11232	9838	17880	5120

n	19681	19682	19683	19684	19685	19686	19687	19688	19689	19690
φ(n)	19680	9072	13122	7776	15120	6144	19686	9328	13124	7120

n	19691	19692	19693	19694	19695	19696	19697	19698	19699	19700
φ(n)	16128	6552	19228	9576	9600	9840	19696	5544	19698	7840

n	19701	19702	19703	19704	19705	19706	19707	19708	19709	19710
φ(n)	11880	9850	17280	6560	13488	9628	13136	9072	19708	5184

n	19711	19712	19713	19714	19715	19716	19717	19718	19719	19720
φ(n)	18832	7680	13140	9856	15768	6240	19716	9858	11232	7168

n	19721	19722	19723	19724	19725	19726	19727	19728	19729	19730
φ(n)	17280	6192	17820	9860	10480	8448	19726	6528	19440	7888

n	19731	19732	19733	19734	19735	19736	19737	19738	19739	19740
φ(n)	13152	9864	16908	5280	15784	9864	12096	9660	19738	4416

n	19741	19742	19743	19744	19745	19746	19747	19748	19749	19750
φ(n)	18684	9870	13160	9856	14320	6576	15120	9872	12656	7800

n	19751	19752	19753	19754	19755	19756	19757	19758	19759	19760
φ(n)	19750	6576	19752	7872	10512	8960	18876	6336	19758	6912

n	19761	19762	19763	19764	19765	19766	19767	19768	19769	19770
φ(n)	11280	9600	19762	6480	15312	9882	11960	8448	19344	5264

n	19771	19772	19773	19774	19775	19776	19777	19778	19779	19780
φ(n)	18592	9884	12168	9886	13440	6528	19776	8400	12456	7392

n	19781	19782	19783	19784	19785	19786	19787	19788	19789	19790
φ(n)	19500	5616	19440	9888	10544	9120	19320	6144	15360	7912

n	19791	19792	19793	19794	19795	19796	19797	19798	19799	19800
φ(n)	13176	9888	19792	6596	15264	8400	13196	9360	18264	4800

n	19801	19802	19803	19804	19805	19806	19807	19808	19809	19810
φ(n)	19800	9900	10560	9900	14848	6600	19096	9888	12600	6768

n	19811	19812	19813	19814	19815	19816	19817	19818	19819	19820
φ(n)	18000	6048	19812	9906	10560	9904	15984	6588	19818	7920

n	19821	19822	19823	19824	19825	19826	19827	19828	19829	19830
φ(n)	13212	8320	19320	5568	14400	9460	13212	9912	19500	5280

n	19831	19832	19833	19834	19835	19836	19837	19838	19839	19840
φ(n)	16992	9504	12000	9660	15864	6048	19516	7776	12416	7680

n	19841	19842	19843	19844	19845	19846	19847	19848	19849	19850
φ(n)	19840	6612	19842	8800	9072	9922	19536	6608	18964	7920

n	19851	19852	19853	19854	19855	19856	19857	19858	19859	19860
φ(n)	12192	8496	19852	6612	13680	9216	13236	9928	17016	5280

n	19861	19862	19863	19864	19865	19866	19867	19868	19869	19870
φ(n)	19860	9930	13236	9120	15232	5040	19866	9932	12816	7944

n	19871	19872	19873	19874	19875	19876	19877	19878	19879	19880
φ(n)	19200	6336	15936	9396	10400	9936	16560	6624	19584	6720

n	19881	19882	19883	19884	19885	19886	19887	19888	19889	19890
φ(n)	12972	9940	19488	6624	15360	9720	11352	8960	19888	4608

n	19891	19892	19893	19894	19895	19896	19897	19898	19899	19900
φ(n)	19890	9944	12528	8232	15136	6624	19600	9948	11880	7920

n	19901	19902	19903	19904	19905	19906	19907	19908	19909	19910
φ(n)	17052	6360	18360	9920	10608	9648	18720	5616	19404	7200

n	19911	19912	19913	19914	19915	19916	19917	19918	19919	19920
φ(n)	13272	9360	19912	6636	13632	9168	13272	9504	19918	5248

n	19921	19922	19923	19924	19925	19926	19927	19928	19929	19930
φ(n)	18100	8532	12768	9344	15920	6480	19926	9568	10368	7968

n	19931	19932	19933	19934	19935	19936	19937	19938	19939	19940
φ(n)	18864	6000	19260	9966	10608	8448	19936	6644	19656	7968

n	19941	19942	19943	19944	19945	19946	19947	19948	19949	19950
φ(n)	11968	9048	15120	6624	15952	9972	12960	9972	19948	4320

n	19951	19952	19953	19954	19955	19956	19957	19958	19959	19960
φ(n)	19600	9408	13284	9060	14688	6648	17100	9376	13304	7968

n	19961	19962	19963	19964	19965	19966	19967	19968	19969	19970
φ(n)	19960	6648	19962	7920	9680	9768	19440	6144	18900	7984

n	19971	19972	19973	19974	19975	19976	19977	19978	19979	19980
φ(n)	11376	9984	19972	6656	14720	9040	13316	8556	19978	5184

n	19981	19982	19983	19984	19985	19986	19987	19988	19989	19990
φ(n)	17472	9792	13320	9984	13680	6660	17160	9432	13320	7992

n	19991	19992	19993	19994	19995	19996	19997	19998	19999	20000
φ(n)	19990	5376	19992	9216	10080	9996	19996	6000	17136	8000

J.P. Martin-Flatin