Voozh

A318323

Numerators of rational valued sequence whose Dirichlet convolution with itself yields A046523, smallest number with same prime signature as n.

1, 1, 1, 3, 1, 2, 1, 5, 3, 2, 1, 5, 1, 2, 2, 35, 1, 5, 1, 5, 2, 2, 1, 4, 3, 2, 5, 5, 1, 9, 1, 63, 2, 2, 2, 35, 1, 2, 2, 4, 1, 9, 1, 5, 5, 2, 1, 55, 3, 5, 2, 5, 1, 4, 2, 4, 2, 2, 1, 9, 1, 2, 5, 231, 2, 9, 1, 5, 2, 9, 1, 43, 1, 2, 5, 5, 2, 9, 1, 55, 35, 2, 1, 9, 2, 2, 2, 4, 1, 9, 2, 5, 2, 2, 2, 49, 1, 5, 5, 35, 1, 9, 1, 4, 9

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OFFSET

1,4

COMMENTS

The first 2^20 terms are positive.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A046523(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

PROG

(PARI)

up_to = 16384;