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A325515
Sum of sums of omegas of the parts over all strict integer partitions of n.
4
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.
FORMULA
a(n) = A001222(A325504(n)).
MATHEMATICA
Table[Sum[Total[PrimeOmega/@s], {s, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 07 2019
STATUS
approved