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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A318507 A055807 A213060 * A054024 A144644 A151509

Adjacent sequences:  A272005 A272006 A272007 * A272009 A272010 A272011

KEYWORD

nonn,frac

AUTHOR

Michel Marcus, May 10 2016

STATUS

approved

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)