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A078635 Number of partitions of n into perfect powers. 6
1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 5, 5, 7, 8, 8, 8, 12, 14, 15, 15, 19, 21, 22, 22, 28, 33, 35, 37, 43, 48, 50, 52, 62, 70, 75, 79, 92, 100, 105, 109, 126, 140, 148, 157, 177, 194, 202, 211, 237, 261, 276, 290, 324, 351, 370, 384, 424, 462, 489, 514, 562, 609, 640, 670, 728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..64.

FORMULA

G.f.: Product_{k=i^j, i>=1, j>=2, excluding duplicates} 1/(1 - x^k). - Ilya Gutkovskiy, Mar 21 2017

EXAMPLE

a(10)=5 since 10 can be written as 9+1, 8+1+1, 4+4+1+1, 4+1+1+1+1+1+1, or 1+1+1+1+1+1+1+1+1+1.

MATHEMATICA

t = Union[Flatten[Table[n^k, {n, 1, 60}, {k, 2, 10}]]]; p[n_] := IntegerPartitions[n, All, t]; Table[p[n], {n, 0, 12}] (*shows partitions*)

a[n_] := Length@p@n; a /@ Range[0, 80]

(* Clark Kimberling, Mar 09 2014 *)

CROSSREFS

Cf. A001597.

Cf. A131799.

Sequence in context: A230447 A029078 A131799 * A286305 A046768 A274151

Adjacent sequences:  A078632 A078633 A078634 * A078636 A078637 A078638

KEYWORD

nonn

AUTHOR

Henry Bottomley, Dec 12 2002

STATUS

approved

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Last modified May 7 14:09 EDT 2021. Contains 343650 sequences. (Running on oeis4.)