A272008 a(n) is the numerator of the fractional part of sigma(n)/n, where sigma(n) is the sum of the divisors of n.

0, 1, 1, 3, 1, 0, 1, 7, 4, 4, 1, 1, 1, 5, 3, 15, 1, 1, 1, 1, 11, 7, 1, 1, 6, 8, 13, 0, 1, 2, 1, 31, 5, 10, 13, 19, 1, 11, 17, 1, 1, 2, 1, 10, 11, 13, 1, 7, 8, 43, 7, 23, 1, 2, 17, 1, 23, 16, 1, 4, 1, 17, 41, 63, 19, 2, 1, 29, 9, 2, 1, 17, 1, 20, 49, 16, 19, 2, 1, 13, 40

Offset

1,4

Comments

a(n) = 0 when n is a multiply-perfect number (A007691).

a(n) = 1 when n is a prime or if n belongs to A215012.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

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

Example

The sum of divisors of 4 is 7; its abundancy is 7/4 = 1 + 3/4 so a(4) = 3.

Mathematica

f[n_] := Numerator[FractionalPart[DivisorSigma[1, n]/n]]; Array[f, 81] (* Robert G. Wilson v, Nov 24 2016 *)

Prog

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

Crossrefs

Cf. A000203, A007691, A017665, A017666, A108775, A215012, A240923, A243473.

Sequence in context: A055807 A364285 A213060 * A054024 A144644 A151509

Adjacent sequences: A272005 A272006 A272007 * A272009 A272010 A272011

Keyword

nonn,frac

Author

Michel Marcus, May 10 2016

Status

approved