A306433 Number of partitions of n into 2 distinct prime powers (not including 1).

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

Links

Table of n, a(n) for n=0..95.

Index entries for sequences related to partitions

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}]

Crossrefs

Cf. A000961, A071330, A106244, A117929, A246655, A307726, A307825.

Sequence in context: A082533 A230149 A050373 * A308174 A126237 A243164

Adjacent sequences: A306430 A306431 A306432 * A306434 A306435 A306436

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 30 2019

Status

approved