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A306433 Number of partitions of n into 2 distinct prime powers (not including 1). 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 8 17:40 EDT 2020. Contains 335524 sequences. (Running on oeis4.)