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%I #28 Mar 04 2018 10:35:37
%S 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,
%T 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,
%U 1,17,41,63,19,2,1,29,9,2,1,17,1,20,49,16,19,2,1,13,40
%N a(n) is the numerator of the fractional part of sigma(n)/n, where sigma(n) is the sum of the divisors of n.
%C a(n) = 0 when n is a multiply-perfect number (A007691).
%C a(n) = 1 when n is a prime or if n belongs to A215012.
%H Antti Karttunen, <a href="/A272008/b272008.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A017665(n) mod A017666(n).
%e The sum of divisors of 4 is 7; its abundancy is 7/4 = 1 + 3/4 so a(4) = 3.
%t f[n_] := Numerator[FractionalPart[DivisorSigma[1, n]/n]]; Array[f, 81] (* _Robert G. Wilson v_, Nov 24 2016 *)
%o (PARI) a(n) = my(ab = sigma(n)/n); numerator(ab) % denominator(ab);
%Y Cf. A000203, A007691, A017665, A017666, A108775, A215012, A240923, A243473.
%K nonn,frac
%O 1,4
%A _Michel Marcus_, May 10 2016
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