OFFSET
1,2
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.
The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.
EXAMPLE
The terms together with their prime indices begin:
1: {}
2: {1}
3: {2}
4: {1,1}
6: {1,2}
7: {4}
8: {1,1,1}
10: {1,3}
12: {1,1,2}
15: {2,3}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
MATHEMATICA
nn=1000;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
ots[y_]:=Sum[i*y[[i]], {i, Length[y]}];
seq=Table[ots[primeMS[n]], {n, 1, nn}];
Select[Range[nn], FreeQ[seq[[Range[#-1]]], seq[[#]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2023
STATUS
approved