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A307726
Number of partitions of n into 2 prime powers (not including 1).
4
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
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]
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Apr 24 2019
STATUS
approved