A326812 - OEIS

A326812

Expansion of Sum_{k>=1} (2^k - 1) * x^(2^k - 1) / (1 - x^(2^k - 1)).

1, 1, 4, 1, 1, 4, 8, 1, 4, 1, 1, 4, 1, 8, 19, 1, 1, 4, 1, 1, 11, 1, 1, 4, 1, 1, 4, 8, 1, 19, 32, 1, 4, 1, 8, 4, 1, 1, 4, 1, 1, 11, 1, 1, 19, 1, 1, 4, 8, 1, 4, 1, 1, 4, 1, 8, 4, 1, 1, 19, 1, 32, 74, 1, 1, 4, 1, 1, 4, 8, 1, 4, 1, 1, 19, 1, 8, 4, 1, 1, 4, 1, 1, 11, 1

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OFFSET

1,3

COMMENTS

Sum of divisors of n of the form 2^j - 1 for j >= 1.

LINKS

Table of n, a(n) for n=1..85.

FORMULA

L.g.f.: -log(Product_{n>=1} (1 - x^(2^n - 1))) = Sum_{n>=1} a(n) * x^n / n.

exp(Sum_{n>=1} a(n) * x^n / n) = g.f. for A000929.

exp(Sum_{n>=1} (-1)^(n + 1) * a(n) * x^n / n) = g.f. for A079559.

a(n) = Sum_{d|n} A036987(d) * d.