OFFSET
1,1
COMMENTS
EXAMPLE
The prime indices of 24 are {1,1,1,2} with (1+1+1+1) = 4 or (1+1)+(2) = 4 or (2+2) = 4, so 24 is not in the sequence.
The terms together with their prime indices begin:
3: {2} 43: {14} 85: {3,7}
5: {3} 47: {15} 89: {24}
7: {4} 49: {4,4} 91: {4,6}
11: {5} 53: {16} 95: {3,8}
13: {6} 55: {3,5} 97: {25}
17: {7} 59: {17} 99: {2,2,5}
19: {8} 61: {18} 101: {26}
23: {9} 63: {2,2,4} 103: {27}
25: {3,3} 65: {3,6} 107: {28}
27: {2,2,2} 67: {19} 109: {29}
29: {10} 71: {20} 113: {30}
31: {11} 73: {21} 115: {3,9}
35: {3,4} 77: {4,5} 117: {2,2,6}
37: {12} 79: {22} 119: {4,7}
41: {13} 83: {23} 121: {5,5}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
combs[n_, y_]:=With[{s=Table[{k, i}, {k, y}, {i, 0, Floor[n/k]}]}, Select[Tuples[s], Total[Times@@@#]==n&]];
Select[Range[100], combs[PrimeOmega[#], Union[prix[#]]]=={}&]
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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KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 15 2023
STATUS
approved