OFFSET
1,1
COMMENTS
EXAMPLE
The prime indices of 24 are {1,1,1,2} with submultiset {1,1,2} summing to 4, so 24 is not in the sequence.
The terms together with their prime indices begin:
3: {2} 29: {10} 58: {1,10}
5: {3} 31: {11} 59: {17}
7: {4} 34: {1,7} 61: {18}
10: {1,3} 35: {3,4} 62: {1,11}
11: {5} 37: {12} 63: {2,2,4}
13: {6} 38: {1,8} 65: {3,6}
14: {1,4} 41: {13} 67: {19}
17: {7} 43: {14} 68: {1,1,7}
19: {8} 44: {1,1,5} 71: {20}
22: {1,5} 46: {1,9} 73: {21}
23: {9} 47: {15} 74: {1,12}
25: {3,3} 49: {4,4} 76: {1,1,8}
26: {1,6} 52: {1,1,6} 77: {4,5}
27: {2,2,2} 53: {16} 79: {22}
28: {1,1,4} 55: {3,5} 82: {1,13}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], FreeQ[Total/@prix/@Divisors[#], PrimeOmega[#]]&]
CROSSREFS
The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum or linear combination of the parts. The current sequence is starred.
sum-full sum-free comb-full comb-free
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Triangles:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 15 2023
STATUS
approved