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A317832 Denominators of rational valued sequence f whose Dirichlet convolution with itself yields A000203 (sigma, the sum of divisors).

%I A317832 #9 May 09 2025 10:17:40
%S A317832 1,2,1,8,1,1,1,16,2,2,1,4,1,1,1,128,1,4,1,8,1,1,1,8,1,2,1,2,1,1,1,256,
%T A317832 1,2,1,16,1,1,1,16,1,1,1,4,2,1,1,64,2,2,1,8,1,2,1,4,1,2,1,4,1,1,1,
%U A317832 1024,1,1,1,8,1,1,1,32,1,2,1,4,1,1,1,128,8,2,1,1,1,1,1,8,1,4,1,2,1,1,1,128,1,4,1,8,1,1,1,16,1
%N A317832 Denominators of rational valued sequence f whose Dirichlet convolution with itself yields A000203 (sigma, the sum of divisors).
%H A317832 Antti Karttunen, <a href="/A317832/b317832.txt">Table of n, a(n) for n = 1..16384</a>
%H A317832 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A317832 a(n) = denominator 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 A317832 (PARI)
%o A317832 A317831perA317832(n) = if(1==n,n,(sigma(n)-sumdiv(n,d,if((d>1)&&(d<n),A317831perA317832(d)*A317831perA317832(n/d),0)))/2);
%o A317832 A317832(n) = denominator(A317831perA317832(n));
%o A317832 (PARI) for(n=1, 100, print1(denominator(direuler(p=2, n, 1/((1-p*X)*(1-X))^(1/2))[n]), ", ")) \\ _Vaclav Kotesovec_, May 09 2025
%Y A317832 Cf. A317831 (gives the numerators).
%Y A317832 Cf. also A000203, A299152.
%K A317832 nonn,frac
%O A317832 1,2
%A A317832 _Antti Karttunen_, Aug 10 2018