A307726 Number of partitions of n into 2 prime powers (not including 1).

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

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 A365742

Adjacent sequences: A307723 A307724 A307725 * A307727 A307728 A307729

Keyword

nonn,look

Author

Ilya Gutkovskiy, Apr 24 2019

Status

approved