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

1,4

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A263756 A204984 A335341 * A325969 A325826 A081297

Adjacent sequences: A243470 A243471 A243472 * A243474 A243475 A243476

Keyword

nonn

Author

Michel Marcus, Jun 05 2014

Status

approved