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A323053
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Number of integer partitions of n with no 1's such that no part is a power of any other (unequal) part.
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4
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1, 0, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 15, 19, 25, 30, 38, 47, 58, 71, 87, 106, 131, 156, 190, 228, 275, 328, 394, 468, 556, 661, 784, 923, 1089, 1283, 1507, 1766, 2068, 2416, 2821, 3284, 3822, 4438, 5148, 5961, 6898, 7968, 9195, 10593, 12198, 14019, 16102, 18472
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OFFSET
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0,5
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LINKS
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EXAMPLE
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The a(2) = 1 through a(11) = 12 integer partitions (A = 10, B = 11):
(2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(22) (32) (33) (43) (44) (54) (55) (65)
(222) (52) (53) (63) (64) (74)
(322) (62) (72) (73) (83)
(332) (333) (433) (92)
(2222) (522) (532) (443)
(3222) (622) (533)
(3322) (632)
(22222) (722)
(3332)
(5222)
(32222)
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MATHEMATICA
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stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[IntegerPartitions[n], And[FreeQ[#, 1], stableQ[#, IntegerQ[Log[#1, #2]]&]]&]], {n, 30}]
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CROSSREFS
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Cf. A001597, A002865, A007916, A052410, A101417, A102430, A108917, A305148, A305630, A305631, A321346, A323093.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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