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

Author

Michel Marcus, May 10 2016

Keywords

• nonn
• frac

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.

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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