A307825 Number of partitions of n into 3 distinct prime powers (not including 1).

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 4, 4, 5, 4, 6, 5, 7, 6, 8, 8, 10, 8, 10, 9, 12, 11, 12, 11, 15, 12, 15, 14, 17, 17, 20, 18, 19, 19, 19, 22, 23, 20, 21, 24, 23, 24, 24, 24, 27, 28, 24, 27, 28, 28, 28, 33, 27, 33, 29, 31, 30, 35, 27, 35, 33, 34, 31, 40, 32, 42, 35, 39, 35, 47, 32

Offset: 0

Author

Ilya Gutkovskiy, Apr 30 2019

Keywords

• nonn

Examples

			a(15) = 4 because we have [9, 4, 2], [8, 5, 2], [8, 4, 3] and [7, 5, 3].
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000961, A106244, A125688, A246655, A306433, A307727.

Programs

Mathematica

Table[Count[IntegerPartitions[n, {3}], _?(And[UnsameQ @@ #, AllTrue[#, PrimePowerQ[#] &]] &)], {n, 0, 78}]

Formula

a(n) = [x^n y^3] Product_{k>=1} (1 + y*x^A246655(k)).