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A317938 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001222 (bigomega n) + A063524 (1, 0, 0, 0, ...).

%I A317938 #5 Aug 23 2018 21:02:23
%S A317938 1,1,1,7,1,3,1,17,7,3,1,11,1,3,3,139,1,11,1,11,3,3,1,15,7,3,17,11,1,3,
%T A317938 1,263,3,3,3,17,1,3,3,15,1,3,1,11,11,3,1,83,7,11,3,11,1,15,3,15,3,3,1,
%U A317938 -3,1,3,11,995,3,3,1,11,3,3,1,11,1,3,11,11,3,3,1,83,139,3,1,-3,3,3,3,15,1,-3,3,11,3,3,3,189,1,11,11,17,1,3,1,15,3
%N A317938 Numerators of rational valued sequence whose Dirichlet convolution with itself yields sequence A001222 (bigomega n) + A063524 (1, 0, 0, 0, ...).
%H A317938 Antti Karttunen, <a href="/A317938/b317938.txt">Table of n, a(n) for n = 1..65537</a>
%F A317938 a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A001222(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
%o A317938 (PARI)
%o A317938 A317938aux(n) = if(1==n,n,(bigomega(n)-sumdiv(n,d,if((d>1)&&(d<n),A317938aux(d)*A317938aux(n/d),0)))/2);
%o A317938 A317938(n) = numerator(A317938aux(n));
%o A317938 (PARI)
%o A317938 \\ Memoized implementation:
%o A317938 memo317938 = Map();
%o A317938 A317938aux(n) = if(1==n,n,if(mapisdefined(memo317938,n),mapget(memo317938,n),my(v = (bigomega(n)-sumdiv(n,d,if((d>1)&&(d<n),A317938aux(d)*A317938aux(n/d),0)))/2); mapput(memo317938,n,v); (v)));
%Y A317938 Cf. A001222, A063524, A046644 (denominators).
%Y A317938 Cf. also A317831, A317925, A317933, A317845, A317846, A317937.
%K A317938 sign,frac
%O A317938 1,4
%A A317938 _Antti Karttunen_, Aug 12 2018