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A074971 Number of partitions of n into distinct parts of order n. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A300826 A305936 A211111 * A198067 A282749 A132587

Adjacent sequences:  A074968 A074969 A074970 * A074972 A074973 A074974

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 05 2002

STATUS

approved

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Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)