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A367397
Numbers m such that bigomega(m) is the sum of prime indices of some semiprime divisor of m.
8
4, 12, 18, 30, 36, 40, 42, 54, 60, 66, 78, 81, 90, 100, 102, 112, 114, 120, 126, 135, 138, 140, 150, 168, 174, 180, 186, 189, 198, 210, 220, 222, 225, 234, 246, 250, 252, 258, 260, 270, 280, 282, 297, 300, 306, 315, 318, 330, 336, 340, 342, 350, 351, 352, 354
OFFSET
1,1
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.
These are the Heinz numbers of the partitions counted by A367394.
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], MemberQ[Total/@Subsets[prix[#], {2}], PrimeOmega[#]]&]
CROSSREFS
The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum, linear combination, or semi-sum of the parts. The current sequence is starred.
sum-full sum-free comb-full comb-free semi-full semi-free
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A325761 ranks partitions whose length is a part, counted by A002865.
A088809 and A093971 count subsets containing semi-sums.
A236912 counts partitions with no semi-sum of the parts, ranks A364461.
A237113 counts partitions with a semi-sum of the parts, ranks A364462.
A304792 counts subset-sums of partitions, strict A365925.
A366738 counts semi-sums of partitions, strict A366741.
Triangles:
A365381 counts subsets with a subset summing to k, complement A366320.
A365541 counts subsets with a semi-sum k.
A367404 counts partitions with a semi-sum k, strict A367405.
Sequence in context: A071929 A008037 A301251 * A062859 A300745 A305240
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 21 2023
STATUS
approved