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A323094
Number of strict integer partitions of n where no part is 2^k times any other part, for any k > 0.
8
1, 1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 7, 8, 10, 12, 12, 15, 17, 20, 24, 27, 33, 35, 41, 48, 54, 61, 69, 79, 87, 101, 113, 128, 144, 159, 181, 201, 225, 251, 281, 311, 347, 388, 428, 477, 525, 579, 643, 712, 788, 868, 954, 1051, 1155, 1272, 1398, 1534, 1682, 1840, 2016
OFFSET
0,5
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400
EXAMPLE
The a(1) = 1 through a(12) = 8 strict integer partitions (A = 10, B = 11, C = 12):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
(31) (32) (51) (43) (53) (54) (64) (65) (75)
(52) (62) (72) (73) (74) (93)
(61) (71) (531) (91) (83) (A2)
(532) (92) (B1)
(A1) (543)
(731) (651)
(732)
MATHEMATICA
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&stableQ[#, IntegerQ[Log[2, #1/#2]]&]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 04 2019
STATUS
approved