cp's OEIS Frontend

A317935 Numerators of rational valued sequence whose Dirichlet convolution with itself yields A003557, n divided by largest squarefree divisor of n.

%I A317935 #10 Aug 24 2018 22:12:19
%S A317935 1,1,1,7,1,1,1,25,11,1,1,7,1,1,1,363,1,11,1,7,1,1,1,25,19,1,61,7,1,1,
%T A317935 1,1335,1,1,1,77,1,1,1,25,1,1,1,7,11,1,1,363,27,19,1,7,1,61,1,25,1,1,
%U A317935 1,7,1,1,11,9923,1,1,1,7,1,1,1,275,1,1,19,7,1,1,1,363,1363,1,1,7,1,1,1,25,1,11,1,7,1,1,1,1335,1,27,11,133,1,1,1,25,1
%N A317935 Numerators of rational valued sequence whose Dirichlet convolution with itself yields A003557, n divided by largest squarefree divisor of n.
%C A317935 Multiplicative because A003557 is.
%C A317935 No negative terms among the first 2^20 terms. Is the sequence nonnegative?
%H A317935 Antti Karttunen, <a href="/A317935/b317935.txt">Table of n, a(n) for n = 1..65537</a>
%H A317935 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dirichlet_convolution">Dirichlet convolution</a>
%F A317935 a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A003557(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
%o A317935 (PARI)
%o A317935 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2]--); factorback(f); }; \\ From A003557
%o A317935 A317935aux(n) = if(1==n,n,(A003557(n)-sumdiv(n,d,if((d>1)&&(d<n),A317935aux(d)*A317935aux(n/d),0)))/2);
%o A317935 A317935(n) = numerator(A317935aux(n));
%Y A317935 Cf. A003557, A046644 (denominators).
%Y A317935 Cf. also A300717, A300719, A318317.
%K A317935 nonn,frac,mult
%O A317935 1,4
%A A317935 _Antti Karttunen_, Aug 12 2018