OFFSET
1,2
COMMENTS
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {} 43: {14} 91: {4,6} 141: {2,15}
2: {1} 46: {1,9} 94: {1,15} 142: {1,20}
3: {2} 47: {15} 95: {3,8} 143: {5,6}
5: {3} 49: {4,4} 97: {25} 145: {3,10}
7: {4} 53: {16} 98: {1,4,4} 147: {2,4,4}
11: {5} 57: {2,8} 101: {26} 149: {35}
13: {6} 58: {1,10} 103: {27} 151: {36}
14: {1,4} 59: {17} 106: {1,16} 157: {37}
17: {7} 61: {18} 107: {28} 158: {1,22}
19: {8} 65: {3,6} 109: {29} 159: {2,16}
21: {2,4} 67: {19} 111: {2,12} 161: {4,9}
23: {9} 69: {2,9} 113: {30} 163: {38}
26: {1,6} 71: {20} 115: {3,9} 167: {39}
29: {10} 73: {21} 119: {4,7} 169: {6,6}
31: {11} 74: {1,12} 122: {1,18} 173: {40}
35: {3,4} 77: {4,5} 127: {31} 178: {1,24}
37: {12} 79: {22} 131: {32} 179: {41}
38: {1,8} 83: {23} 133: {4,8} 181: {42}
39: {2,6} 87: {2,10} 137: {33} 182: {1,4,6}
41: {13} 89: {24} 139: {34} 183: {2,18}
For example, the prime indices of 95 are {3,8}, of which only 3 is in the sequence, so 95 is in the sequence.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
aQ[n_]:=Length[Cases[primeMS[n], _?aQ]]<=1;
Select[Range[100], aQ]
CROSSREFS
Contains all prime numbers A000040.
Numbers S without all prime indices in S are A324694.
Numbers S without any prime indices in S are A324695.
Numbers S with exactly one prime index in S are A331785.
Numbers S with at most one distinct prime index in S are A331912.
Numbers S with exactly one distinct prime index in S are A331913.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 01 2020
STATUS
approved