A317940 Numerators of sequence whose Dirichlet convolution with itself yields A046644.

1, 1, 1, 7, 1, 1, 1, 9, 7, 1, 1, 7, 1, 1, 1, 427, 1, 7, 1, 7, 1, 1, 1, 9, 7, 1, 9, 7, 1, 1, 1, 471, 1, 1, 1, 49, 1, 1, 1, 9, 1, 1, 1, 7, 7, 1, 1, 427, 7, 7, 1, 7, 1, 9, 1, 9, 1, 1, 1, 7, 1, 1, 7, 4099, 1, 1, 1, 7, 1, 1, 1, 63, 1, 1, 7, 7, 1, 1, 1, 427, 427, 1, 1, 7, 1, 1, 1, 9, 1, 7, 1, 7, 1, 1, 1, 471, 1, 7, 7, 49, 1, 1, 1, 9, 1

Offset

1,4

Comments

Multiplicative because A046644 is.

No negative terms among the first 2^20 terms. Is the sequence nonnegative?

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A046644(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

Prog

(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.
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A046644(n) = factorback(apply(e -> 2^A005187(e), factor(n)[, 2]));
v317940aux = DirSqrt(vector(up_to, n, A046644(n)));
A317940(n) = numerator(v317940aux[n]);

Crossrefs

Cf. A005187, A046644, A317934 (denominators), A317941.

Sequence in context: A365332 A367483 A348281 * A318674 A284118 A165725

Adjacent sequences: A317937 A317938 A317939 * A317941 A317942 A317943

Keyword

nonn,frac,mult

Author

Antti Karttunen, Aug 14 2018

Status

approved