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Product of means of integer partitions with Heinz numbers from 2 to n.
1

%I #5 Sep 29 2019 00:26:37

%S 1,2,2,6,9,36,36,72,144,720,960,5760,14400,36000,36000,252000,420000,

%T 3360000,5600000,16800000,50400000,453600000,567000000,1701000000,

%U 5953500000,11907000000,23814000000,238140000000,476280000000,5239080000000,5239080000000

%N Product of means of integer partitions with Heinz numbers from 2 to n.

%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

%F a(n > 2) = a(n - 1) * A326567(n) / A326568(n).

%e We have a(7) = 1 * 2 * 1 * 3 * 3/2 * 4 = 36.

%t Table[Product[Total[Cases[FactorInteger[k],{p_,k_}:>k*PrimePi[p]]]/PrimeOmega[k],{k,2,n}],{n,2,30}]

%Y Partial products of A326567/A326568.

%Y Cf. A056239, A112798, A316413, A327474, A327482, A327486.

%K nonn

%O 2,2

%A _Gus Wiseman_, Sep 28 2019