OFFSET
1,2
COMMENTS
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {} 84: {1,1,2,4}
3: {2} 88: {1,1,1,5}
4: {1,1} 90: {1,2,2,3}
9: {2,2} 100: {1,1,3,3}
10: {1,3} 108: {1,1,2,2,2}
12: {1,1,2} 112: {1,1,1,1,4}
16: {1,1,1,1} 120: {1,1,1,2,3}
27: {2,2,2} 144: {1,1,1,1,2,2}
28: {1,1,4} 160: {1,1,1,1,1,3}
30: {1,2,3} 192: {1,1,1,1,1,1,2}
36: {1,1,2,2} 208: {1,1,1,1,6}
40: {1,1,1,3} 243: {2,2,2,2,2}
48: {1,1,1,1,2} 252: {1,1,2,2,4}
64: {1,1,1,1,1,1} 256: {1,1,1,1,1,1,1,1}
81: {2,2,2,2} 264: {1,1,1,2,5}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], EvenQ[Total[primeMS[#]]]&&PrimeOmega[#]>=Total[primeMS[#]]/2&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 22 2021
STATUS
approved