A318658 - OEIS

A318658

Denominators of the sequence whose Dirichlet convolution with itself yields A087003, a(2n) = 0 and a(2n+1) = moebius(2n+1).

1, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 8, 1, 16, 1, 2, 1, 2, 1, 4, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 16, 1, 2, 1, 8, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 1, 2, 1, 16, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 16, 1, 4, 1, 2, 1, 128, 1, 2, 1, 4, 1, 4, 1, 2, 1, 4, 1, 4, 1, 4, 1, 2, 1, 16, 1, 2, 1, 2, 1, 8

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

The sequence seems to give the denominators of several other similarly constructed "Dirichlet Square Roots".

LINKS

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

FORMULA

a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A087003(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

a(n) = 2^A318659(n).

a(2n) = 1, a(2n-1) = A046644(2n-1) = A318512(2n-1), for all n >= 1.

PROG