cp's OEIS Frontend

A317845 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001065 (sum of proper divisors) + A063524 (1, 0, 0, 0, ...).

%I A317845 #5 Aug 23 2018 21:03:27
%S A317845 1,1,1,11,1,11,1,45,15,15,1,95,1,19,17,659,1,131,1,135,21,27,1,315,23,
%T A317845 31,89,175,1,125,1,2319,29,39,25,901,1,43,33,455,1,165,1,255,215,51,1,
%U A317845 3739,31,291,41,295,1,671,33,595,45,63,1,731,1,67,271,16319,37,245,1,375,53,237,1,2135,1,79,335,415,37,285,1,5419,1979,87,1
%N A317845 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001065 (sum of proper divisors) + A063524 (1, 0, 0, 0, ...).
%C A317845 The first negative term is a(360) = -12947.
%H A317845 Antti Karttunen, <a href="/A317845/b317845.txt">Table of n, a(n) for n = 1..65537</a>
%F A317845 a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A001065(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
%o A317845 (PARI)
%o A317845 A317845aux(n) = if(1==n,n,((sigma(n)-n)-sumdiv(n,d,if((d>1)&&(d<n),A317845aux(d)*A317845aux(n/d),0)))/2);
%o A317845 A317845(n) = numerator(A317845aux(n));
%Y A317845 Cf. A001065, A063524, A046644 (denominators).
%Y A317845 Cf. also A317831, A317846.
%K A317845 sign,frac
%O A317845 1,4
%A A317845 _Antti Karttunen_, Aug 12 2018