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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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..58.

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}]

CROSSREFS

Cf. A001597, A007916, A025147, A052410, A078374, A087897, A120641, A275972, A303362, A323053, A323087, A323088.

Sequence in context: A282611 A187498 A029137 * A027157 A112194 A238788

Adjacent sequences:  A323051 A323052 A323053 * A323055 A323056 A323057

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 04 2019

STATUS

approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)