A330106 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A330106

Number of integer partitions of n whose product is a powerful number.

0, 0, 0, 0, 2, 2, 5, 5, 9, 11, 18, 19, 30, 36, 51, 62, 87, 104, 141, 171, 225, 271, 349, 419, 534, 643, 804, 965, 1197, 1431, 1766, 2106, 2571, 3063, 3719, 4410, 5325, 6305, 7567, 8939, 10678, 12572, 14961, 17567, 20804, 24389, 28775, 33626, 39551, 46106

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..49.

EXAMPLE

The a(4) = 2 through a(10) = 18 partitions:

(4) (41) (33) (331) (8) (9) (55)

(22) (221) (42) (421) (44) (81) (82)

(222) (2221) (422) (333) (91)

(411) (4111) (2222) (441) (433)

(2211) (22111) (3311) (4221) (442)

(4211) (22221) (811)

(22211) (33111) (3322)

(41111) (42111) (3331)

(221111) (222111) (4222)

(411111) (4411)

(2211111) (22222)

(42211)

(222211)

(331111)

(421111)

(2221111)

(4111111)

(22111111)

MATHEMATICA

powQ[n_]:=Min@@Last/@FactorInteger[n]>1;

Table[Length[Select[IntegerPartitions[n], powQ[Times@@#]&]], {n, 0, 30}]

CROSSREFS

The strict version is A330216.

Powerful numbers are A001694.

Partitions whose product is a perfect power are A320322.

Cf. A000041, A001055, A001597, A003963, A064573, A320325.

Sequence in context: A213675 A321185 A320322 * A214795 A287744 A214253

Adjacent sequences: A330103 A330104 A330105 * A330107 A330108 A330109

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 05 2019

STATUS

approved