%I #15 May 08 2016 22:42:25

%S 0,1,1,3,1,1,1,7,4,4,1,4,1,5,3,15,1,7,1,11,11,7,1,3,6,8,13,1,1,7,1,31,

%T 5,10,13,55,1,11,17,5,1,9,1,10,11,13,1,19,8,43,7,23,1,11,17,8,23,16,1,

%U 9,1,17,41,63,19,13,1,29,9,37,1,41,1,20,49,16

%N a(n) = numerator(sigma(n)/n) - denominator(sigma(n)/n) where sigma(n) = sum of divisors of n.

%C a(n) = 1 for n prime or perfect (A053813).

%C a(n) = A001065(n) when n is in A014567.

%C a(n) > n for n in A069057. - _Michel Marcus_, May 04 2016

%H Michel Marcus, <a href="/A243473/b243473.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A017665(n) - A017666(n).

%t f[n_] := DivisorSigma[1, n]/n; Table[Numerator[f@ n] - Denominator[f@ n], {n, 76}] (* _Michael De Vlieger_, Sep 09 2015 *)

%o (PARI) a(n) = numerator(ab = sigma(n)/n) - denominator(ab);

%Y Cf. A000203, A001065, A014567, A017665, A017666, A053813, A069057.

%K nonn

%O 1,4

%A _Michel Marcus_, Jun 05 2014