A070160 - OEIS

%I #14 Jun 01 2024 22:12:25

%S 4,9,15,25,35,49,95,119,121,143,169,209,287,289,319,323,361,377,527,

%T 529,559,779,841,899,903,923,961,989,1007,1189,1199,1343,1349,1369,

%U 1681,1763,1849,1919,2159,2209,2507,2759,2809,2911,3239,3481,3599,3721

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

%C Euler phi value divided by Chowla function gives integer.

%H Donovan Johnson, <a href="/A070160/b070160.txt">Table of n, a(n) for n = 1..10000</a>

%F {k : A000010(k)/A048050(k) is integer}.

%e 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 Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n-1); If[IntegerQ[s], Print[n]], {n, 2, 100000}]

%Y Cf. A000010, A001065, A000203, A020492, A068418, A062972, A055940, A070159, A070037.

%Y Union of A000040 (primes) and A070161.

%K nonn

%O 1,1

%A _Labos Elemer_, Apr 26 2002