cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A070160 Nonprime numbers k such that phi(k)/(sigma(k) - k - 1) is an integer.

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%I A070160 #17 Jan 10 2025 10:08:29
%S A070160 4,9,15,25,35,49,95,119,121,143,169,209,287,289,319,323,361,377,527,
%T A070160 529,559,779,841,899,903,923,961,989,1007,1189,1199,1343,1349,1369,
%U A070160 1681,1763,1849,1919,2159,2209,2507,2759,2809,2911,3239,3481,3599,3721
%N A070160 Nonprime numbers k such that phi(k)/(sigma(k) - k - 1) is an integer.
%C A070160 Euler phi value divided by Chowla function gives integer.
%H A070160 Donovan Johnson, <a href="/A070160/b070160.txt">Table of n, a(n) for n = 1..10000</a>
%F A070160 {k : A000010(k)/A048050(k) is an integer}.
%e A070160 In A062972, n=15: q = 8/8 = 1; n=101: q = 100/1 = 100. While integer quotient chowla(n)/phi(n) gives only 5 nonprime solutions below 20000000 (see A070037), here, the integer reciprocals, q = phi(n)/chowla(n) obtained with squared primes and with other composites. If n=p^2, q = p(p-1)/p = p-1. So for squared primes, the quotients give A006093.
%t A070160 Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n-1); If[IntegerQ[s], Print[n]], {n, 2, 100000}]
%Y A070160 Cf. A000010, A001065, A000203, A020492, A068418, A062972, A055940, A070159, A070037.
%Y A070160 Union of A000040 (primes) and A070161.
%K A070160 nonn
%O A070160 1,1
%A A070160 _Labos Elemer_, Apr 26 2002