A307825 - OEIS

%I #6 Apr 30 2019 21:50:13

%S 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,

%T 11,15,12,15,14,17,17,20,18,19,19,19,22,23,20,21,24,23,24,24,24,27,28,

%U 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

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

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

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

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

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

%K nonn

%O 0,13

%A _Ilya Gutkovskiy_, Apr 30 2019