A327485 Product of means of integer partitions with Heinz numbers from 2 to n.

1, 2, 2, 6, 9, 36, 36, 72, 144, 720, 960, 5760, 14400, 36000, 36000, 252000, 420000, 3360000, 5600000, 16800000, 50400000, 453600000, 567000000, 1701000000, 5953500000, 11907000000, 23814000000, 238140000000, 476280000000, 5239080000000, 5239080000000

Offset: 2

Author

Gus Wiseman, Sep 28 2019

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

Partial products of A326567/A326568.

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

Programs

Mathematica

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

Formula

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