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.
EXAMPLE
The terms together with their prime indices begin:
1: {}
12: {1,1,2}
70: {1,3,4}
90: {1,2,2,3}
112: {1,1,1,1,4}
144: {1,1,1,1,2,2}
286: {1,5,6}
325: {3,3,6}
462: {1,2,4,5}
520: {1,1,1,3,6}
525: {2,3,3,4}
594: {1,2,2,2,5}
646: {1,7,8}
675: {2,2,2,3,3}
832: {1,1,1,1,1,1,6}
840: {1,1,1,2,3,4}
For example, 525 has prime indices {2,3,3,4}, and 3+3 = 2+4, so 525 is in the sequence.
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Total[Select[prix[#], OddQ]]==Total[Select[prix[#], EvenQ]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2023
STATUS
approved