A317832 - OEIS

%I #7 Aug 10 2018 09:06:06

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

%H Antti Karttunen, <a href="/A317832/b317832.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) = 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 (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 A317832(n) = denominator(A317831perA317832(n));

%Y Cf. A317831 (gives the numerators).

%Y Cf. also A000203, A299152.

%K nonn,frac

%O 1,2

%A _Antti Karttunen_, Aug 10 2018