The On-Line Encyclopedia of Integer Sequences (OEIS)

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A322527

Number of integer partitions of n whose product of parts is a power of a squarefree number (A072774).
(history; published version)

#6 by Susanna Cuyler at Fri Dec 14 21:20:35 EST 2018

STATUS

proposed

approved

#5 by Gus Wiseman at Fri Dec 14 11:56:34 EST 2018

STATUS

editing

proposed

#4 by Gus Wiseman at Fri Dec 14 11:56:07 EST 2018

EXAMPLE

Missing from the list for n = 7 through 9:

(43) (62) (54)

(322) (332) (63)

(431) (432)

(3221) (522)

(621)

(3222)

(3321)

(4311)

(32211)

#3 by Gus Wiseman at Fri Dec 14 08:30:06 EST 2018

CROSSREFS

Cf. A003963, A005117, A038041, A062503, A064573, A072774, A295193, A302505, A306021, A319169, A320322, A322526, A322528, A322530.

#2 by Gus Wiseman at Fri Dec 14 07:07:30 EST 2018

NAME

allocated for Gus WisemanNumber of integer partitions of n whose product of parts is a power of a squarefree number (A072774).

DATA

1, 1, 2, 3, 5, 7, 11, 13, 18, 21, 31, 34, 45, 51, 63, 72, 88, 97, 120, 128, 158, 174, 201, 222, 264, 287, 333, 359, 416, 441, 518, 557, 631, 684, 770, 833, 954, 1017, 1141, 1222, 1378, 1475, 1643, 1755, 1939, 2097, 2327, 2471, 2758, 2928, 3233, 3470, 3813, 4085

OFFSET

0,3

EXAMPLE

The a(1) = 1 through a(8) = 18 integer partitions:

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

(11) (21) (22) (32) (33) (52) (44)

(111) (31) (41) (42) (61) (53)

(211) (221) (51) (331) (71)

(1111) (311) (222) (421) (422)

(2111) (321) (511) (521)

(11111) (411) (2221) (611)

(2211) (3211) (2222)

(3111) (4111) (3311)

(21111) (22111) (4211)

(111111) (31111) (5111)

(211111) (22211)

(1111111) (32111)

(41111)

(221111)

(311111)

(2111111)

(11111111)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], SameQ@@Last/@FactorInteger[Times@@#]&]], {n, 30}]

CROSSREFS

Cf. A003963, A005117, A038041, A062503, A064573, A072774, A295193, A302505, A306021, A319169, A320322, A322526.

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, Dec 14 2018

STATUS

approved

editing

#1 by Gus Wiseman at Fri Dec 14 07:07:30 EST 2018

NAME

allocated for Gus Wiseman

KEYWORD

allocated

STATUS

approved