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A318449
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Numerators of the sequence whose Dirichlet convolution with itself yields A001511, the 2-adic valuation of 2n.
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3
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1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 35, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1
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OFFSET
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1,9
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LINKS
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FORMULA
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a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A001511(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
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MATHEMATICA
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a1511[n_] := IntegerExponent[2n, 2];
f[1] = 1; f[n_] := f[n] = 1/2 (a1511[n] - Sum[f[d] f[n/d], {d, Divisors[ n][[2 ;; -2]]}]);
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PROG
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(PARI)
up_to = 65537;
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.
v318449_51 = DirSqrt(vector(up_to, n, A001511(n)));
A318449(n) = numerator(v318449_51[n]);
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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