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

Author

Gus Wiseman, Sep 25 2019

Keywords

• nonn

Examples

			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)
		

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.

Programs

Mathematica

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