login
A331913
Lexicographically earliest sequence containing 1 and all positive integers that have exactly one distinct prime index already in the sequence.
6
1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 19, 23, 25, 26, 27, 31, 32, 39, 49, 52, 53, 58, 59, 64, 65, 67, 74, 81, 82, 83, 86, 87, 91, 94, 97, 101, 103, 104, 111, 116, 117, 121, 122, 123, 125, 127, 128, 129, 131, 141, 142, 143, 145, 146, 148, 158, 164, 167, 172, 178
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 sequence of terms together with their prime indices begins:
1: {} 52: {1,1,6} 116: {1,1,10}
2: {1} 53: {16} 117: {2,2,6}
3: {2} 58: {1,10} 121: {5,5}
4: {1,1} 59: {17} 122: {1,18}
5: {3} 64: {1,1,1,1,1,1} 123: {2,13}
7: {4} 65: {3,6} 125: {3,3,3}
8: {1,1,1} 67: {19} 127: {31}
9: {2,2} 74: {1,12} 128: {1,1,1,1,1,1,1}
11: {5} 81: {2,2,2,2} 129: {2,14}
16: {1,1,1,1} 82: {1,13} 131: {32}
17: {7} 83: {23} 141: {2,15}
19: {8} 86: {1,14} 142: {1,20}
23: {9} 87: {2,10} 143: {5,6}
25: {3,3} 91: {4,6} 145: {3,10}
26: {1,6} 94: {1,15} 146: {1,21}
27: {2,2,2} 97: {25} 148: {1,1,12}
31: {11} 101: {26} 158: {1,22}
32: {1,1,1,1,1} 103: {27} 164: {1,1,13}
39: {2,6} 104: {1,1,1,6} 167: {39}
49: {4,4} 111: {2,12} 172: {1,1,14}
MATHEMATICA
aQ[n_]:=n==1||Length[Select[PrimePi/@First/@FactorInteger[n], aQ]]==1;
Select[Range[200], aQ]
CROSSREFS
Contains all prime powers A000961.
Numbers S without all prime indices in S are A324694.
Numbers S without any prime indices in S are A324695.
Numbers S with at most one prime index in S are A331784.
Numbers S with exactly one prime index in S are A331785.
Numbers S with at most one distinct prime index in S are A331912.
Sequence in context: A099627 A324841 A184155 * A318612 A318690 A302498
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 01 2020
STATUS
approved