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A323088 Number of strict integer partitions of n using numbers that are not perfect powers. 3
1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 3, 3, 4, 5, 5, 7, 7, 9, 11, 11, 15, 16, 18, 22, 24, 27, 32, 34, 41, 45, 51, 59, 64, 75, 82, 94, 105, 116, 132, 146, 163, 183, 202, 225, 251, 277, 309, 341, 378, 417, 463, 510, 564, 622, 685, 754, 830, 914, 1001, 1103, 1207, 1325 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..61.

FORMULA

O.g.f.: Product_{n in A007916} (1 + x^n).

EXAMPLE

A list of all strict integer partitions using numbers that are not perfect powers begins:

   2: (2)        11: (6,3,2)    15: (13,2)       17: (12,5)

   3: (3)        12: (12)       15: (12,3)       17: (12,3,2)

   5: (5)        12: (10,2)     15: (10,5)       17: (11,6)

   5: (3,2)      12: (7,5)      15: (10,3,2)     17: (10,7)

   6: (6)        12: (7,3,2)    15: (7,6,2)      17: (10,5,2)

   7: (7)        13: (13)       15: (7,5,3)      17: (7,5,3,2)

   7: (5,2)      13: (11,2)     16: (14,2)       18: (18)

   8: (6,2)      13: (10,3)     16: (13,3)       18: (15,3)

   8: (5,3)      13: (7,6)      16: (11,5)       18: (13,5)

   9: (7,2)      13: (6,5,2)    16: (11,3,2)     18: (13,3,2)

   9: (6,3)      14: (14)       16: (10,6)       18: (12,6)

  10: (10)       14: (12,2)     16: (7,6,3)      18: (11,7)

  10: (7,3)      14: (11,3)     16: (6,5,3,2)    18: (11,5,2)

  10: (5,3,2)    14: (7,5,2)    17: (17)         18: (10,6,2)

  11: (11)       14: (6,5,3)    17: (15,2)       18: (10,5,3)

  11: (6,5)      15: (15)       17: (14,3)       18: (7,6,5)

MATHEMATICA

perpowQ[n_]:=GCD@@FactorInteger[n][[All, 2]]>1;

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&FreeQ[#, 1]&&And@@Not/@perpowQ/@#&]], {n, 20}]

CROSSREFS

Cf. A001597, A007916, A025147, A052410, A087897, A305631, A321346, A323054, A323089, A323090.

Sequence in context: A084840 A029278 A125950 * A052954 A123505 A320779

Adjacent sequences:  A323085 A323086 A323087 * A323089 A323090 A323091

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 04 2019

STATUS

approved

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Last modified July 11 01:51 EDT 2020. Contains 335600 sequences. (Running on oeis4.)