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

1,2

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

Formula

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

Prog

(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));

Crossrefs

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

Sequence in context: A141822 A033099 A330833 * A337331 A018892 A343654

Adjacent sequences: A378433 A378434 A378435 * A378437 A378438 A378439

Keyword

nonn

Author

Antti Karttunen, Nov 26 2024

Status

approved