A327779 Number of integer partitions of n whose LCM is greater than n.

1, 0, 0, 0, 0, 1, 0, 2, 3, 7, 9, 18, 16, 31, 42, 61, 87, 133, 169, 246, 302, 411, 545, 738, 874, 1167, 1497, 1945, 2421, 3110, 3498, 4476, 5615, 7061, 8777, 10925, 12957, 16036, 19644, 24061, 28858, 35177, 41572, 50424, 60643, 72953, 87499, 104893, 123821, 147776

Offset

0,8

Links

Table of n, a(n) for n=0..49.

Example

The a(5) = 1 through a(12) = 16 partitions (empty columns not shown):
  (32)  (43)  (53)   (54)    (64)     (65)      (75)
        (52)  (431)  (72)    (73)     (74)      (543)
              (521)  (432)   (433)    (83)      (651)
                     (522)   (532)    (92)      (732)
                     (531)   (541)    (443)     (741)
                     (4311)  (721)    (533)     (831)
                     (5211)  (4321)   (542)     (921)
                             (5311)   (641)     (5322)
                             (43111)  (722)     (5331)
                                      (731)     (5421)
                                      (4322)    (7221)
                                      (4331)    (7311)
                                      (5321)    (53211)
                                      (5411)    (54111)
                                      (7211)    (72111)
                                      (43211)   (531111)
                                      (53111)
                                      (431111)

Mathematica

Table[Length[Select[IntegerPartitions[n], LCM@@#>n&]], {n, 30}]

Crossrefs

The Heinz numbers of these partitions are given by A327784.

Partitions whose LCM is a multiple of their sum are A327778.

Partitions whose LCM is equal to their sum are A074761.

Partitions whose LCM is less than their sum are A327781.

Cf. A018818, A067538, A290103, A326842, A327780, A327783.

Sequence in context: A327066 A165803 A378925 * A291740 A204520 A358392

Adjacent sequences: A327776 A327777 A327778 * A327780 A327781 A327782

Keyword

nonn

Author

Gus Wiseman, Sep 25 2019

Status

approved