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%I #8 Aug 10 2018 09:05:56
%S 1,3,2,19,3,3,4,63,9,9,6,19,7,6,6,867,9,27,10,57,8,9,12,63,11,21,11,
%T 19,15,9,16,3069,12,27,12,171,19,15,14,189,21,12,22,57,27,18,24,867,
%U 41,33,18,133,27,33,18,63,20,45,30,57,31,24,18,22199,21,18,34,171,24,18,36,567,37,57,22,95,24,21,40,2601,227,63,42,19,27,33
%N Numerators of rational valued sequence f whose Dirichlet convolution with itself yields A000203 (sigma, the sum of divisors).
%H Antti Karttunen, <a href="/A317831/b317831.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A000203(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
%o (PARI)
%o A317831perA317832(n) = if(1==n,n,(sigma(n)-sumdiv(n,d,if((d>1)&&(d<n),A317831perA317832(d)*A317831perA317832(n/d),0)))/2);
%o A317831(n) = numerator(A317831perA317832(n));
%Y Cf. A317832 (gives the denominators).
%Y Cf. also A000203, A299151.
%K nonn,frac
%O 1,2
%A _Antti Karttunen_, Aug 10 2018
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