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A307726 Number of partitions of n into 2 prime powers (not including 1). 3
0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 4, 4, 4, 2, 4, 3, 4, 4, 4, 3, 5, 3, 6, 4, 7, 4, 7, 2, 5, 4, 6, 3, 5, 3, 5, 5, 6, 2, 7, 3, 7, 4, 6, 2, 8, 3, 7, 4, 6, 2, 7, 3, 6, 4, 7, 2, 9, 2, 7, 5, 7, 2, 9, 3, 7, 6, 7, 3, 9, 2, 8, 4, 6, 4, 10, 3, 9, 4, 7, 3, 11, 4, 8, 3, 7, 2, 10, 2, 8, 3, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for sequences related to partitions

FORMULA

a(n) = [x^n y^2] Product_{k>=1} 1/(1 - y*x^A246655(k)).

EXAMPLE

a(10) = 3 because we have [8, 2], [7, 3] and [5, 5].

MAPLE

# note that this requires A246655 to be pre-computed

f:= proc(n, k, pmax) option remember;

  local t, p, j;

  if n = 0 then return `if`(k=0, 1, 0) fi;

  if k = 0 then return 0 fi;

  if n > k*pmax then return 0 fi;

  t:= 0:

  for p in A246655 do

    if p > pmax then return t fi;

    t:= t + add(procname(n-j*p, k-j, min(p-1, n-j*p)), j=1..min(k, floor(n/p)))

  od;

  t

end proc:

map(f, [$0..100]); # Robert Israel, Apr 29 2019

MATHEMATICA

Array[Count[IntegerPartitions[#, {2}], _?(AllTrue[#, PrimePowerQ] &)] &, 101, 0]

CROSSREFS

Cf. A000961, A023894, A061358, A071068, A071330, A071331, A246655, A280242, A307727.

Sequence in context: A076634 A083277 A274011 * A235123 A242768 A064557

Adjacent sequences:  A307723 A307724 A307725 * A307727 A307728 A307729

KEYWORD

nonn,look

AUTHOR

Ilya Gutkovskiy, Apr 24 2019

STATUS

approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)