A243473 a(n) = numerator(sigma(n)/n) - denominator(sigma(n)/n) where sigma(n) = sum of divisors of n.

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

Offset: 1

Author

Michel Marcus, Jun 05 2014

Keywords

• nonn

Comments

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

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

a(n) > n for n in A069057. - Michel Marcus, May 04 2016

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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