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A300580 Number of partitions of n into prime power parts (not including 1) that do not divide n. 3

%I

%S 1,0,0,0,0,1,0,3,1,3,2,11,1,18,6,9,5,43,5,65,7,31,30,137,5,115,59,84,

%T 26,379,19,519,42,213,197,323,23,1267,340,489,50,2213,107,2897,221,

%U 375,938,4871,61,3733,662,2193,553,10218,409,4241,310,4341,3685,20586,154,25792,5635,2862,990,12806

%N Number of partitions of n into 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(10) = 2 because we have [7, 3] and [4, 3, 3].

%t Table[SeriesCoefficient[Product[1/(1 - Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 65}]

%Y Cf. A023894, A098743, A128515, A246655, A284289, A300584.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Mar 09 2018

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Last modified June 18 18:06 EDT 2021. Contains 345120 sequences. (Running on oeis4.)