OFFSET
0,2
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.
EXAMPLE
The prime indices of 84 are y = {1,1,2,4}, with even sum 8; but 8/2 = 4 is in y, so 84 is not in the sequence.
The terms together with their prime indices begin:
1: {}
3: {2}
7: {4}
10: {1,3}
13: {6}
16: {1,1,1,1}
19: {8}
21: {2,4}
22: {1,5}
27: {2,2,2}
28: {1,1,4}
29: {10}
34: {1,7}
36: {1,1,2,2}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], EvenQ[Total[prix[#]]]&&FreeQ[prix[#], Total[prix[#]]/2]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 13 2023
STATUS
approved