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

0,4

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.

Links

Table of n, a(n) for n=0..43.

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A291100 A361271 A082290 * A182984 A301798 A093840

Adjacent sequences: A325533 A325534 A325535 * A325537 A325538 A325539

Keyword

nonn

Author

Gus Wiseman, May 08 2019

Status

approved