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A131799 Number of partitions of n into parts that are squares or cubes. 7
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, 61, 69, 74, 78, 90, 98, 103, 107, 122, 135, 143, 152, 170, 186, 194, 203, 225, 247, 261, 275, 305, 330, 348, 362, 396, 429, 454, 477, 519, 561, 590, 618, 666, 717 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) = A078635(n) for n < 32 = 2^5.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: Product_{k>=1} (1 - x^(k^6)) / ((1 - x^(k^2)) * (1 - x^(k^3))). - Vaclav Kotesovec, Jan 12 2017

EXAMPLE

a(10) = #{9+1, 8+1+1, 4+4+1+1, 4+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1} = 5.

MATHEMATICA

nmax = 65; c2max = nmax^(1/2); c3max = nmax^(1/3);

s = Flatten[{Table[n^2, {n, 1, c2max}]}~Join~{Table[n^3, {n, 1, c3max}]}];

Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Jul 31 2020 *)

CROSSREFS

Cf. A000041, A001156, A002760, A003108, A078635.

Sequence in context: A125584 A230447 A029078 * A078635 A286305 A046768

Adjacent sequences:  A131796 A131797 A131798 * A131800 A131801 A131802

KEYWORD

nonn,changed

AUTHOR

Reinhard Zumkeller, Jul 16 2007

EXTENSIONS

a(0)=1 prepended by Ilya Gutkovskiy, Jan 11 2017

STATUS

approved

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Last modified August 14 18:32 EDT 2020. Contains 336483 sequences. (Running on oeis4.)