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A300584 Number of partitions of n into distinct prime power parts (not including 1) that do not divide n. 3

%I

%S 1,0,0,0,0,1,0,2,1,2,1,4,1,5,2,4,3,8,2,11,4,6,6,18,3,13,10,10,8,35,7,

%T 42,9,20,24,22,10,72,33,35,11,102,21,120,29,26,65,161,16,117,56,93,52,

%U 246,43,113,36,139,160,370,39,422,208,102,62,216,110,613,145,305,130,780,57,878

%N Number of partitions of n into distinct prime power parts (not including 1) that do not divide n.

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

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

%t Table[SeriesCoefficient[Product[(1 + Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 73}]

%Y Cf. A054685, A200745, A209402, A246655, A300580.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Mar 09 2018

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)