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 A074971 Number of partitions of n into distinct parts of order n. 11
 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: A339790 A334924 A211111 * A344008 A198067 A282749 Adjacent sequences:  A074968 A074969 A074970 * A074972 A074973 A074974 KEYWORD nonn AUTHOR Vladeta Jovovic, Oct 05 2002 STATUS approved

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Last modified September 20 08:10 EDT 2021. Contains 347577 sequences. (Running on oeis4.)