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A306433
Number of partitions of n into 2 distinct prime powers (not including 1).
2
0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 4, 4, 3, 2, 4, 3, 3, 4, 4, 3, 5, 3, 5, 4, 6, 4, 7, 2, 4, 4, 6, 3, 5, 3, 5, 5, 5, 2, 7, 3, 6, 4, 6, 2, 7, 3, 7, 4, 5, 2, 7, 3, 5, 4, 6, 2, 9, 2, 7, 5, 7, 2, 9, 3, 6, 6, 7, 3, 9, 2, 8, 4, 5, 4, 10, 3, 8, 4, 7, 3, 11, 4, 8, 3, 6, 2
OFFSET
0,8
FORMULA
a(n) = [x^n y^2] Product_{k>=1} (1 + y*x^A246655(k)).
EXAMPLE
a(12) = 3 because we have [9, 3], [8, 4] and [7, 5].
MATHEMATICA
Table[Count[IntegerPartitions[n, {2}], _?(And[UnsameQ @@ #, AllTrue[#, PrimePowerQ[#] &]] &)], {n, 0, 95}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 30 2019
STATUS
approved