%I #7 Aug 11 2018 22:00:57
%S 1,3,2,19,4,2,11,63,6,3,19,13,23,17,5,867,16,4,35,5,17,25,21,11,31,29,
%T 13,113,27,13,57,3069,13,9,23,25,71,41,14,69,79,33,41,169,9,25,89,615,
%U 259,53,17,197,51,25,29,389,20,31,113,59,117,67,10,22199,18,14,131,31,51,71,69,11,143,77,22,281,91,35,153,489,71,85,81,151,19
%N Numerators of rational valued sequence whose Dirichlet convolution with itself yields A005187.
%C The first negative term is a(330) = -21.
%H Antti Karttunen, <a href="/A317927/b317927.txt">Table of n, a(n) for n = 1..16384</a>
%F a(n) = numerator 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 (PARI)
%o A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A317927perA317928(n) = if(1==n,n,(A005187(n)-sumdiv(n,d,if((d>1)&&(d<n),A317927perA317928(d)*A317927perA317928(n/d),0)))/2);
%o A317927(n) = numerator(A317927perA317928(n));
%o (PARI)
%o \\ Memoized implementation:
%o memo = Map();
%o A317927perA317928(n) = if(1==n,n,if(mapisdefined(memo,n),mapget(memo,n),my(v = (A005187(n)-sumdiv(n,d,if((d>1)&&(d<n),A317927perA317928(d)*A317927perA317928(n/d),0)))/2); mapput(memo,n,v); (v)));
%Y Cf. A005187, A317928 (denominators).
%Y Cf. also A297111, A300244, A299151, A317931.
%K sign,frac
%O 1,2
%A _Antti Karttunen_, Aug 11 2018
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