A325515 Sum of sums of omegas of the parts over all strict integer partitions of n.

0, 0, 1, 2, 3, 5, 8, 11, 14, 22, 29, 37, 50, 63, 81, 106, 129, 160, 203, 246, 303, 373, 449, 541, 654, 782, 932, 1116, 1322, 1559, 1848, 2167, 2537, 2978, 3470, 4041, 4706, 5449, 6303, 7291, 8402, 9665, 11117, 12744, 14592, 16708, 19062, 21730, 24757, 28141

Offset

0,4

Comments

Also omega of the product of products of parts over all strict 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..49.

Formula

a(n) = A001222(A325504(n)).

Mathematica

Table[Sum[Total[PrimeOmega/@s], {s, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 30}]

Crossrefs

Cf. A001222, A003963, A015716, A015723, A022629, A056239, A066189, A112798, A147655, A246867, A325504, A325506.

Sequence in context: A194221 A054925 A194248 * A126097 A024611 A131073

Adjacent sequences: A325512 A325513 A325514 * A325516 A325517 A325518

Keyword

nonn

Author

Gus Wiseman, May 07 2019

Status

approved