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A317928 Denominators of rational valued sequence whose Dirichlet convolution with itself yields A005187.

%I A317928 #6 Aug 11 2018 22:01:10
%S A317928 1,2,1,8,1,1,2,16,1,1,2,4,2,4,1,128,1,1,2,1,2,4,1,2,2,4,1,16,1,2,2,
%T A317928 256,1,1,2,4,2,4,1,8,2,4,1,16,1,2,2,64,8,4,1,16,1,2,2,32,1,2,2,8,2,4,
%U A317928 1,1024,1,1,2,2,2,4,1,1,2,4,1,16,4,2,2,32,2,4,1,16,1,2,2,32,1,2,4,8,2,4,1,64,2,16,1,16,1,2,2,32,2
%N A317928 Denominators of rational valued sequence whose Dirichlet convolution with itself yields A005187.
%H A317928 Antti Karttunen, <a href="/A317928/b317928.txt">Table of n, a(n) for n = 1..16384</a>
%F A317928 a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A005187(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
%o A317928 (PARI)6
%o A317928 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A317928 A317927perA317928(n) = if(1==n,n,(A005187(n)-sumdiv(n,d,if((d>1)&&(d<n),A317927perA317928(d)*A317927perA317928(n/d),0)))/2);
%o A317928 A317928(n) = denominator(A317927perA317928(n));
%Y A317928 Cf. A005187, A317927 (numerators).
%Y A317928 Cf. also A297111, A300244, A299152, A317932.
%K A317928 nonn,frac
%O A317928 1,2
%A A317928 _Antti Karttunen_, Aug 11 2018