OFFSET
1,2
COMMENTS
EXAMPLE
The term 42 is in the sequence because it has 7 proper divisors (1, 2, 3, 6, 7, 14, 21) and its sum of prime indices is also 1 + 2 + 4 = 7.
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
32: {1,1,1,1,1}
42: {1,2,4}
54: {1,2,2,2}
56: {1,1,1,4}
64: {1,1,1,1,1,1}
100: {1,1,3,3}
128: {1,1,1,1,1,1,1}
162: {1,2,2,2,2}
176: {1,1,1,1,5}
204: {1,1,2,7}
234: {1,2,2,6}
256: {1,1,1,1,1,1,1,1}
MATHEMATICA
Select[Range[100], DivisorSigma[0, #]-1==Total[Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved