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 A327781 Number of integer partitions of n whose LCM is less than n. 6
 0, 0, 1, 2, 4, 5, 9, 12, 18, 22, 30, 37, 52, 69, 89, 110, 143, 163, 204, 243, 298, 374, 451, 516, 620, 790, 932, 1064, 1243, 1454, 1699, 2365, 2733, 3071, 3524, 3945, 4526, 5600, 6361, 7111, 8057, 9405, 10621, 12836, 14395, 16066, 18047, 19860, 22143, 25748 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 EXAMPLE The a(2) = 1 through a(8) = 18 partitions:   (11)  (21)   (22)    (41)     (33)      (61)       (44)         (111)  (31)    (221)    (42)      (322)      (62)                (211)   (311)    (51)      (331)      (71)                (1111)  (2111)   (222)     (421)      (332)                        (11111)  (411)     (511)      (422)                                 (2211)    (2221)     (611)                                 (3111)    (3211)     (2222)                                 (21111)   (4111)     (3221)                                 (111111)  (22111)    (3311)                                           (31111)    (4211)                                           (211111)   (5111)                                           (1111111)  (22211)                                                      (32111)                                                      (41111)                                                      (221111)                                                      (311111)                                                      (2111111)                                                      (11111111) MAPLE a:= proc(m) option remember; local b; b:=       proc(n, i, l) option remember; `if`(n=0, 1,        `if`(i>1, b(n, i-1, l), 0) +(h-> `if`(h0, b(m\$2, 1), 0)     end: seq(a(n), n=0..70);  # Alois P. Heinz, Oct 10 2019 MATHEMATICA Table[Length[Select[IntegerPartitions[n], LCM@@#1, b[n, i - 1, l], 0] + Function[h, If[h0, b[m, m, 1], 0]]; a /@ Range[0, 70] (* Jean-François Alcover, May 18 2021, after Alois P. Heinz *) PROG (PARI) b(m, n)={my(d=divisors(m)); polcoef(1/prod(i=1, #d, 1 - x^d[i] + O(x*x^n)), n)} a(n)={sum(m=1, n-1, b(m, n)*sum(i=1, (n-1)\m, moebius(i)))} \\ Andrew Howroyd, Oct 09 2019 CROSSREFS The Heinz numbers of these partitions are given by A327776. Partitions whose LCM is equal to their sum are A074761. Partitions whose LCM is greater than their sum are A327779. Cf. A018818, A290103, A316413, A319333, A326842, A327778, A327780. Sequence in context: A241444 A082592 A241339 * A241411 A211373 A241734 Adjacent sequences:  A327778 A327779 A327780 * A327782 A327783 A327784 KEYWORD nonn AUTHOR Gus Wiseman, Sep 25 2019 STATUS approved

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Last modified July 25 03:36 EDT 2021. Contains 346282 sequences. (Running on oeis4.)