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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..59.

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}]

CROSSREFS

Cf. A018819, A087897, A120641, A276431, A303362, A323054, A323092, A323093.

Sequence in context: A240321 A054861 A187324 * A086227 A302402 A079438

Adjacent sequences:  A323091 A323092 A323093 * A323100 A323101 A323102

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 04 2019

STATUS

approved

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Last modified May 21 02:55 EDT 2019. Contains 323434 sequences. (Running on oeis4.)