]> Euler's Totient Function for n = 18001..19000

Euler's Totient Function for n = 18001..19000

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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	18001	18002	18003	18004	18005	18006	18007	18008	18009	18010
φ(n)	17572	9000	11264	7704	13248	6000	16360	9000	11088	7200

n	18011	18012	18013	18014	18015	18016	18017	18018	18019	18020
φ(n)	14760	5616	18012	9006	9600	8992	17556	4320	17496	6656

n	18021	18022	18023	18024	18025	18026	18027	18028	18029	18030
φ(n)	12012	9010	17688	6000	12240	9012	12012	9012	16280	4800

n	18031	18032	18033	18034	18035	18036	18037	18038	18039	18040
φ(n)	15552	7392	12020	8820	14424	5976	16960	8680	10296	6400

n	18041	18042	18043	18044	18045	18046	18047	18048	18049	18050
φ(n)	18040	5760	18042	8304	9600	7728	18046	5888	18048	6840

n	18051	18052	18053	18054	18055	18056	18057	18058	18059	18060
φ(n)	10920	9024	15468	5568	13728	8640	11088	9028	18058	4032

n	18061	18062	18063	18064	18065	18066	18067	18068	18069	18070
φ(n)	18060	8200	11988	9024	14448	6020	14784	9032	11376	6624

n	18071	18072	18073	18074	18075	18076	18077	18078	18079	18080
φ(n)	16992	6000	15600	7740	9600	9036	18076	5720	17800	7168

n	18081	18082	18083	18084	18085	18086	18087	18088	18089	18090
φ(n)	10080	9040	16536	5440	14464	9042	12056	6912	18088	4752

n	18091	18092	18093	18094	18095	18096	18097	18098	18099	18100
φ(n)	17784	9044	11664	8856	11040	5376	18096	9048	12060	7200

n	18101	18102	18103	18104	18105	18106	18107	18108	18109	18110
φ(n)	17292	5160	17640	8640	8960	8220	17136	6024	14256	7240

n	18111	18112	18113	18114	18115	18116	18117	18118	18119	18120
φ(n)	12072	9024	17748	6036	14488	7752	10800	9058	18118	4800

n	18121	18122	18123	18124	18125	18126	18127	18128	18129	18130
φ(n)	18120	7680	10344	8624	14000	5616	18126	8160	12084	6048

n	18131	18132	18133	18134	18135	18136	18137	18138	18139	18140
φ(n)	18130	6040	18132	9066	8640	9064	15540	6044	15360	7248

n	18141	18142	18143	18144	18145	18146	18147	18148	18149	18150
φ(n)	12092	8832	18142	5184	13680	8820	11528	8352	18148	4400

n	18151	18152	18153	18154	18155	18156	18157	18158	18159	18160
φ(n)	15552	9072	12096	8736	14520	5632	17820	7776	12104	7232

n	18161	18162	18163	18164	18165	18166	18167	18168	18169	18170
φ(n)	15120	6048	17680	8568	8256	8760	17640	6048	18168	6864

n	18171	18172	18173	18174	18175	18176	18177	18178	18179	18180
φ(n)	12096	6960	17088	5568	14520	8960	11808	8880	15288	4800

n	18181	18182	18183	18184	18185	18186	18187	18188	18189	18190
φ(n)	18180	9090	10080	9088	14544	5184	16776	9092	11592	6784

n	18191	18192	18193	18194	18195	18196	18197	18198	18199	18200
φ(n)	18190	6048	14784	8260	9696	9096	17580	6048	18198	5760

n	18201	18202	18203	18204	18205	18206	18207	18208	18209	18210
φ(n)	12132	8604	17928	5760	13200	9102	9792	9088	17940	4848

n	18211	18212	18213	18214	18215	18216	18217	18218	18219	18220
φ(n)	18210	8736	11184	7800	14568	5280	18216	9108	12144	7280

n	18221	18222	18223	18224	18225	18226	18227	18228	18229	18230
φ(n)	14688	6072	18222	8448	9720	8400	16560	5040	18228	7288

n	18231	18232	18233	18234	18235	18236	18237	18238	18239	18240
φ(n)	11832	8736	18232	6072	12480	8832	12156	8280	15840	4608

n	18241	18242	18243	18244	18245	18246	18247	18248	18249	18250
φ(n)	16128	7812	12156	9120	14080	6080	17920	9120	9360	7200

n	18251	18252	18253	18254	18255	18256	18257	18258	18259	18260
φ(n)	18250	5616	18252	9126	9728	7776	18256	5696	16740	6560

n	18261	18262	18263	18264	18265	18266	18267	18268	18269	18270
φ(n)	12168	8712	15648	6080	13440	9132	12176	9132	18268	4032

n	18271	18272	18273	18274	18275	18276	18277	18278	18279	18280
φ(n)	16500	9120	12180	9136	13440	6088	15624	7776	12168	7296

n	18281	18282	18283	18284	18285	18286	18287	18288	18289	18290
φ(n)	18000	5520	17848	7824	9152	8880	18286	6048	18288	6960

n	18291	18292	18293	18294	18295	18296	18297	18298	18299	18300
φ(n)	9504	8576	16620	6096	14632	9144	11448	7836	17640	4800

n	18301	18302	18303	18304	18305	18306	18307	18308	18309	18310
φ(n)	18300	9150	12200	7680	12528	6048	18306	8712	11456	7320

n	18311	18312	18313	18314	18315	18316	18317	18318	18319	18320
φ(n)	18310	5184	18312	9156	8640	8640	16896	5880	15696	7296

n	18321	18322	18323	18324	18325	18326	18327	18328	18329	18330
φ(n)	11760	9160	18000	6096	14640	6720	11840	8736	18328	4416

n	18331	18332	18333	18334	18335	18336	18337	18338	18339	18340
φ(n)	17512	9164	10368	8976	13824	6080	16660	8944	12224	6240

n	18341	18342	18343	18344	18345	18346	18347	18348	18349	18350
φ(n)	18340	6108	15744	9168	9776	9172	15720	5520	17980	7320

n	18351	18352	18353	18354	18355	18356	18357	18358	18359	18360
φ(n)	12228	8640	18352	4752	14680	8448	11760	8976	16680	4608

n	18361	18362	18363	18364	18365	18366	18367	18368	18369	18370
φ(n)	15120	9180	12240	9180	14688	6120	18366	7680	11232	6640

n	18371	18372	18373	18374	18375	18376	18377	18378	18379	18380
φ(n)	18370	6120	17388	9186	8400	9184	16192	6120	18378	7344

n	18381	18382	18383	18384	18385	18386	18387	18388	18389	18390
φ(n)	11120	7200	17760	6112	14704	8848	12204	9192	15120	4896

n	18391	18392	18393	18394	18395	18396	18397	18398	18399	18400
φ(n)	17992	7920	12260	8640	13536	5184	18396	9198	12264	7040

n	18401	18402	18403	18404	18405	18406	18407	18408	18409	18410
φ(n)	18400	6132	14280	8904	9792	9202	18096	5568	17920	6288

n	18411	18412	18413	18414	18415	18416	18417	18418	18419	18420
φ(n)	10944	9204	18412	5400	14112	9200	10512	9208	18144	4896

n	18421	18422	18423	18424	18425	18426	18427	18428	18429	18430
φ(n)	16848	9000	11616	7728	13200	5904	18426	8640	12284	6912

n	18431	18432	18433	18434	18435	18436	18437	18438	18439	18440
φ(n)	15792	6144	18432	8496	9824	8360	18156	5256	18438	7360

n	18441	18442	18443	18444	18445	18446	18447	18448	18449	18450
φ(n)	12276	9220	18442	5824	11520	8800	10080	9216	17460	4800

n	18451	18452	18453	18454	18455	18456	18457	18458	18459	18460
φ(n)	18450	7896	12300	9226	14760	6144	18456	8380	10512	6720

n	18461	18462	18463	18464	18465	18466	18467	18468	18469	18470
φ(n)	18460	5760	17928	9216	9840	7908	18096	5832	15840	7384

n	18471	18472	18473	18474	18475	18476	18477	18478	18479	18480
φ(n)	11960	9232	14112	6156	14760	8880	12312	9238	17376	3840

n	18481	18482	18483	18484	18485	18486	18487	18488	18489	18490
φ(n)	18480	9240	12000	9240	14784	5616	14904	9240	12324	7224

n	18491	18492	18493	18494	18495	18496	18497	18498	18499	18500
φ(n)	16400	5808	18492	7920	9792	8704	18096	6164	17064	7200

n	18501	18502	18503	18504	18505	18506	18507	18508	18509	18510
φ(n)	10560	8120	18502	6144	14800	8748	11880	7920	18204	4928

n	18511	18512	18513	18514	18515	18516	18517	18518	18519	18520
φ(n)	18232	8448	10560	9256	12144	6168	18516	9016	12344	7392

n	18521	18522	18523	18524	18525	18526	18527	18528	18529	18530
φ(n)	18520	5292	18522	8400	8640	9048	18240	6144	15876	6912

n	18531	18532	18533	18534	18535	18536	18537	18538	18539	18540
φ(n)	11760	8960	18060	6176	13440	7920	11952	7920	18538	4896

n	18541	18542	18543	18544	18545	18546	18547	18548	18549	18550
φ(n)	18540	9072	10584	8640	14832	5600	17440	9272	12312	6240

n	18551	18552	18553	18554	18555	18556	18557	18558	18559	18560
φ(n)	17112	6176	18552	9276	9888	9276	14400	6180	18216	7168

n	18561	18562	18563	18564	18565	18566	18567	18568	18569	18570
φ(n)	11792	9280	17568	4608	14352	9282	12372	8400	17940	4944

n	18571	18572	18573	18574	18575	18576	18577	18578	18579	18580
φ(n)	15876	9284	12000	9000	14840	6048	17136	7956	11240	7424

n	18581	18582	18583	18584	18585	18586	18587	18588	18589	18590
φ(n)	17472	5832	18582	8800	8352	9292	18586	6192	17920	6240

n	18591	18592	18593	18594	18595	18596	18597	18598	18599	18600
φ(n)	12392	7872	18592	6192	14872	9296	12396	8736	15936	4800

n	18601	18602	18603	18604	18605	18606	18607	18608	18609	18610
φ(n)	15840	9100	11232	9300	14640	5304	17776	9296	12404	7440

n	18611	18612	18613	18614	18615	18616	18617	18618	18619	18620
φ(n)	18072	5520	15948	9040	9216	8544	18616	5936	18144	6048

n	18621	18622	18623	18624	18625	18626	18627	18628	18629	18630
φ(n)	12408	9310	16920	6144	14800	9108	10632	9312	17184	4752

n	18631	18632	18633	18634	18635	18636	18637	18638	18639	18640
φ(n)	18000	8704	12420	7260	14904	6208	18636	9318	11664	7424

n	18641	18642	18643	18644	18645	18646	18647	18648	18649	18650
φ(n)	15972	5712	18360	9048	8960	9322	17976	5184	17536	7440

n	18651	18652	18653	18654	18655	18656	18657	18658	18659	18660
φ(n)	12432	9324	17820	6216	11520	8320	12420	8820	18216	4960

n	18661	18662	18663	18664	18665	18666	18667	18668	18669	18670
φ(n)	18660	7560	12440	9328	14928	5760	16960	8592	10584	7464

n	18671	18672	18673	18674	18675	18676	18677	18678	18679	18680
φ(n)	18670	6208	18340	9336	9840	7392	17676	5640	18678	7456

n	18681	18682	18683	18684	18685	18686	18687	18688	18689	18690
φ(n)	11472	9340	14976	6192	14400	9342	12456	9216	16980	4224

n	18691	18692	18693	18694	18695	18696	18697	18698	18699	18700
φ(n)	18690	9344	11880	8616	14952	5760	16020	9348	11880	6400

n	18701	18702	18703	18704	18705	18706	18707	18708	18709	18710
φ(n)	18700	6228	18328	7968	9408	9108	17256	6232	18304	7480

n	18711	18712	18713	18714	18715	18716	18717	18718	18719	18720
φ(n)	9720	9352	18712	6236	14112	9356	11712	7980	18718	4608

n	18721	18722	18723	18724	18725	18726	18727	18728	18729	18730
φ(n)	18432	7920	12324	9000	12720	6240	18360	9360	12480	7488

n	18731	18732	18733	18734	18735	18736	18737	18738	18739	18740
φ(n)	18730	5328	15600	8064	9984	9360	18240	6228	16056	7488

n	18741	18742	18743	18744	18745	18746	18747	18748	18749	18750
φ(n)	12492	9370	18742	5600	14256	7344	12492	9072	18748	5000

n	18751	18752	18753	18754	18755	18756	18757	18758	18759	18760
φ(n)	17632	9344	9936	9376	13200	6240	18756	9184	11232	6336

n	18761	18762	18763	18764	18765	18766	18767	18768	18769	18770
φ(n)	18432	6032	18088	9380	9936	8520	16044	5632	18632	7504

n	18771	18772	18773	18774	18775	18776	18777	18778	18779	18780
φ(n)	12512	8208	18772	5328	15000	9384	11360	9120	18480	4992

n	18781	18782	18783	18784	18785	18786	18787	18788	18789	18790
φ(n)	16092	9390	12516	9376	13056	6000	18786	7200	12524	7512

n	18791	18792	18793	18794	18795	18796	18797	18798	18799	18800
φ(n)	16632	6048	18792	9396	8544	9072	18796	5760	17080	7360

n	18801	18802	18803	18804	18805	18806	18807	18808	18809	18810
φ(n)	12528	7488	18802	6264	15040	9402	12536	9400	16116	4320

n	18811	18812	18813	18814	18815	18816	18817	18818	18819	18820
φ(n)	17352	9404	12540	8976	14560	5376	18180	9312	11520	7520

n	18821	18822	18823	18824	18825	18826	18827	18828	18829	18830
φ(n)	16240	6272	16128	8640	10000	9412	18480	6264	17820	6432

n	18831	18832	18833	18834	18835	18836	18837	18838	18839	18840
φ(n)	12552	8480	18288	6048	15064	8832	9504	9418	18838	4992

n	18841	18842	18843	18844	18845	18846	18847	18848	18849	18850
φ(n)	18532	9420	11400	8064	15072	6264	18400	8640	12240	6720

n	18851	18852	18853	18854	18855	18856	18857	18858	18859	18860
φ(n)	16152	6280	17728	8560	10032	9424	18576	5376	18858	7040

n	18861	18862	18863	18864	18865	18866	18867	18868	18869	18870
φ(n)	12572	9430	17400	6240	11760	9432	11880	9152	18868	4608

n	18871	18872	18873	18874	18875	18876	18877	18878	18879	18880
φ(n)	18592	8064	12528	9436	15000	5280	18396	9438	10080	7424

n	18881	18882	18883	18884	18885	18886	18887	18888	18889	18890
φ(n)	18564	6288	18040	9440	10064	7560	16000	6288	17424	7552

n	18891	18892	18893	18894	18895	18896	18897	18898	18899	18900
φ(n)	12588	9444	16188	6072	15112	9440	12596	8580	18898	4320

n	18901	18902	18903	18904	18905	18906	18907	18908	18909	18910
φ(n)	18400	8712	12600	8832	14256	5984	15552	9072	11400	7200

n	18911	18912	18913	18914	18915	18916	18917	18918	18919	18920
φ(n)	18910	6272	18912	8064	9216	9456	18916	6300	18918	6720

n	18921	18922	18923	18924	18925	18926	18927	18928	18929	18930
φ(n)	9984	9460	18648	5904	15120	9462	12600	7488	18084	5040

n	18931	18932	18933	18934	18935	18936	18937	18938	18939	18940
φ(n)	17200	9464	12620	9466	12960	6288	18256	8896	12296	7568

n	18941	18942	18943	18944	18945	18946	18947	18948	18949	18950
φ(n)	16560	4800	17928	9216	10080	9472	18946	6312	16236	7560

n	18951	18952	18953	18954	18955	18956	18957	18958	18959	18960
φ(n)	12632	8976	17220	5832	14208	8112	12320	9478	18958	4992

n	18961	18962	18963	18964	18965	18966	18967	18968	18969	18970
φ(n)	18612	8964	10584	8600	15168	6048	17496	9480	12644	6480

n	18971	18972	18973	18974	18975	18976	18977	18978	18979	18980
φ(n)	18600	5760	18972	9256	8800	9472	16260	6324	18978	6912

n	18981	18982	18983	18984	18985	18986	18987	18988	18989	18990
φ(n)	11664	9490	18480	5376	15184	8620	12656	9200	17856	5040

n	18991	18992	18993	18994	18995	18996	18997	18998	18999	19000
φ(n)	16272	9488	11664	9496	14560	6328	17160	7656	12660	7200

J.P. Martin-Flatin