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A323054
Number of strict integer partitions of n with no 1's such that no part is a power of any other part.
8
1, 0, 1, 1, 1, 2, 1, 3, 3, 4, 4, 6, 6, 8, 9, 12, 13, 16, 19, 21, 25, 30, 36, 40, 47, 53, 63, 71, 83, 94, 107, 121, 140, 159, 180, 204, 233, 260, 296, 334, 377, 421, 474, 532, 598, 668, 750, 835, 933, 1038, 1163, 1292, 1435, 1597, 1771, 1966, 2180, 2421, 2673
OFFSET
0,6
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..350
EXAMPLE
The a(2) = 1 through a(13) = 8 strict integer partitions (A = 10, B = 11, C = 12, D = 13):
(2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C) (D)
(32) (43) (53) (54) (64) (65) (75) (76)
(52) (62) (63) (73) (74) (84) (85)
(72) (532) (83) (A2) (94)
(92) (543) (A3)
(632) (732) (B2)
(643)
(652)
MATHEMATICA
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[IntegerPartitions[n], And[FreeQ[#, 1], UnsameQ@@#, stableQ[#, IntegerQ[Log[#1, #2]]&]]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 04 2019
STATUS
approved