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

0,13

Links

Table of n, a(n) for n=0..78.

Index entries for sequences related to partitions

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A123756 A357256 A300755 * A347660 A116648 A152850

Adjacent sequences: A307822 A307823 A307824 * A307826 A307827 A307828

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 30 2019

Status

approved