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: {}
30: {1,2,3}
70: {1,3,4}
154: {1,4,5}
165: {2,3,5}
210: {1,2,3,4}
273: {2,4,6}
286: {1,5,6}
390: {1,2,3,6}
For example, 210 has factorization 14*15, and both factors have the same sum of prime indices 5, so 210 is in the sequence.
MATHEMATICA
sumprix[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]];
Select[Range[1000], SquareFreeQ[#]&&MemberQ[sumprix/@Divisors[#], sumprix[#]/2]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 27 2022
STATUS
approved