|
%I #9 Oct 16 2019 13:14:28
%S 1,0,0,0,0,1,0,2,3,7,9,18,16,31,42,61,87,133,169,246,302,411,545,738,
%T 874,1167,1497,1945,2421,3110,3498,4476,5615,7061,8777,10925,12957,
%U 16036,19644,24061,28858,35177,41572,50424,60643,72953,87499,104893,123821,147776
%N Number of integer partitions of n whose LCM is greater than n.
%e The a(5) = 1 through a(12) = 16 partitions (empty columns not shown):
%e (32) (43) (53) (54) (64) (65) (75)
%e (52) (431) (72) (73) (74) (543)
%e (521) (432) (433) (83) (651)
%e (522) (532) (92) (732)
%e (531) (541) (443) (741)
%e (4311) (721) (533) (831)
%e (5211) (4321) (542) (921)
%e (5311) (641) (5322)
%e (43111) (722) (5331)
%e (731) (5421)
%e (4322) (7221)
%e (4331) (7311)
%e (5321) (53211)
%e (5411) (54111)
%e (7211) (72111)
%e (43211) (531111)
%e (53111)
%e (431111)
%t Table[Length[Select[IntegerPartitions[n],LCM@@#>n&]],{n,30}]
%Y The Heinz numbers of these partitions are given by A327784.
%Y Partitions whose LCM is a multiple of their sum are A327778.
%Y Partitions whose LCM is equal to their sum are A074761.
%Y Partitions whose LCM is less than their sum are A327781.
%Y Cf. A018818, A067538, A290103, A326842, A327780, A327783.
%K nonn
%O 0,8
%A _Gus Wiseman_, Sep 25 2019
|
