A378436 Inverse Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

1, 2, 2, 3, 2, 5, 2, 4, 3, 4, 2, 9, 2, 4, 4, 5, 2, 9, 2, 7, 4, 4, 2, 16, 3, 4, 4, 7, 2, 12, 2, 6, 4, 4, 4, 21, 2, 4, 4, 12, 2, 11, 2, 6, 6, 4, 2, 28, 3, 6, 4, 6, 2, 14, 4, 11, 4, 4, 2, 53, 2, 4, 6, 7, 4, 11, 2, 6, 4, 8, 2, 60, 2, 4, 6, 6, 4, 10, 2, 20, 5, 4, 2, 43, 4, 4, 4, 9, 2, 41, 4, 6, 4, 4, 4, 51, 2, 6, 6, 12

Offset: 1

Author

Antti Karttunen, Nov 26 2024

Keywords

• nonn

Comments

The odd bisection differs from A099774 (the odd bisection of A000005) apparently in the positions given by A005231 (odd abundant numbers): 945, 1575, 2205, 2835, 3465, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000005, A005231, A033630, A099774, A378438 (Dirichlet inverse).

Programs

PARI

A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
A378436(n) = sumdiv(n,d,A033630(d));

Formula

a(n) = Sum_{d|n} A033630(d).