OFFSET
1,1
COMMENTS
First differs from A299729 (non-knapsack) in lacking 525: {2,3,3,4}.
First differs from A325777 in having 462: {1,2,4,5} and lacking 675:{2,2,2,3,3}.
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 partitions containing the sum of some non-singleton submultiset.
EXAMPLE
The terms together with their prime indices begin:
12: {1,1,2}
24: {1,1,1,2}
30: {1,2,3}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
60: {1,1,2,3}
63: {2,2,4}
70: {1,3,4}
72: {1,1,1,2,2}
80: {1,1,1,1,3}
84: {1,1,2,4}
90: {1,2,2,3}
96: {1,1,1,1,1,2}
MATHEMATICA
Select[Range[100], Intersection[prix[#], Total/@Subsets[prix[#], {2, Length[prix[#]]}]]!={}&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 01 2023
STATUS
approved