

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
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OFFSET

1,4


COMMENTS

a(n) = 0 when n is a multiplyperfect 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



