A074971 Number of partitions of n into distinct parts of order n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 6, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 32, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 24, 1, 1, 1, 2, 1, 24, 1, 1, 1, 1, 1, 12, 1, 1, 1, 3, 1, 2

Offset

1,6

Comments

Order of partition is lcm of its parts.

Links

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

Formula

Coefficient of x^n in expansion of Sum_{i divides n} mu(n/i)*Product_{j divides i} (1+x^j).

Example

The a(36) = 6 partitions are (36), (18,12,6), (18,12,4,2), (18,12,3,2,1), (18,9,4,3,2), (12,9,6,4,3,2). - Gus Wiseman, Aug 01 2018

Prog

(PARI) A074971(n) = { my(q=0); fordiv(n, i, my(p=1); fordiv(i, j, p *= (1 + 'x^j)); q += moebius(n/i)*p); polcoeff(q, n); }; \\ Antti Karttunen, Dec 19 2018

Crossrefs

Cf. A000837, A074761, A285572, A290103, A305566, A316431, A316433, A317624.

Cf. also A033630.

Sequence in context: A339790 A334924 A211111 * A344008 A198067 A282749

Adjacent sequences: A074968 A074969 A074970 * A074972 A074973 A074974

Keyword

nonn

Author

Vladeta Jovovic, Oct 05 2002

Status

approved