A325536 Sum of sums of omegas of parts over all integer partitions of n.

0, 0, 1, 2, 6, 9, 19, 28, 51, 75, 119, 170, 261, 362, 525, 723, 1019, 1373, 1890, 2512, 3386, 4452, 5893, 7658, 10017, 12881, 16627, 21210, 27097, 34266, 43392, 54462, 68399, 85285, 106305, 131712, 163132, 200936, 247332, 303066, 370989, 452296, 550875, 668495

Offset: 0

Author

Gus Wiseman, May 08 2019

Keywords

• nonn

Comments

Also omega of the product of products of parts over all integer partitions of n.

The omega of n is A001222(n), the number of prime factors of n counted with multiplicity.

Examples

			The integer partitions of 5 are {(5), (4,1), (3,2), (3,1,1), (2,2,1), (2,1,1,1), (1,1,1,1,1)} with products {5,4,6,3,4,2,1} with product 2880 with omega 9, so a(5) = 9.
		

Crossrefs

Cf. A001222, A006128, A006906, A007870, A066186, A066633, A145519, A215366, A325507.

Programs

Mathematica

Table[Plus@@PrimeOmega/@Join@@IntegerPartitions[n],{n,0,30}]

Formula

a(n) = A001222(A007870(n)).