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 zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.
EXAMPLE
The terms together with their prime indices begin:
1: {}
4: {1,1}
8: {1,1,1}
9: {2,2}
16: {1,1,1,1}
18: {1,2,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
50: {1,3,3}
54: {1,2,2,2}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
81: {2,2,2,2}
100: {1,1,3,3}
108: {1,1,2,2,2}
128: {1,1,1,1,1,1,1}
MATHEMATICA
nn=1000;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]], {i, Length[y]}];
seq=Table[wts[Reverse[primeMS[n]]], {n, 1, nn}];
Select[Range[nn], FreeQ[seq[[Range[#-1]]], seq[[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2023
STATUS
approved