A323093 - OEIS

A323093

Number of integer partitions of n where no part is 2^k times any other part, for any k > 0.

1, 1, 2, 2, 4, 4, 6, 9, 12, 13, 18, 23, 29, 37, 49, 55, 71, 84, 104, 126, 153, 185, 221, 261, 317, 375, 446, 523, 623, 721, 854, 994, 1168, 1357, 1579, 1833, 2126, 2455, 2843, 3270, 3766, 4320, 4980, 5687, 6521, 7444, 8498, 9684, 11039, 12540, 14262

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..50.

EXAMPLE

The a(1) = 1 through a(8) = 12 integer partitions:

(1) (2) (3) (4) (5) (6) (7) (8)

(11) (111) (22) (32) (33) (43) (44)

(31) (311) (51) (52) (53)

(1111) (11111) (222) (61) (62)

(3111) (322) (71)

(111111) (331) (332)

(511) (611)

(31111) (2222)

(1111111) (3311)

(5111)

(311111)

(11111111)

MATHEMATICA

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];

Table[Length[Select[IntegerPartitions[n], stableQ[#, IntegerQ[Log[2, #1/#2]]&]&]], {n, 30}]

CROSSREFS

Cf. A018819, A101417, A120641, A276431, A305148, A323092, A323094.

Sequence in context: A276065 A325253 A143483 * A264788 A192326 A131733

Adjacent sequences: A323090 A323091 A323092 * A323094 A323095 A323096

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 04 2019

STATUS

approved