This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331912 #5 Feb 02 2020 09:04:09
%S A331912 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,26,27,29,31,32,37,39,41,43,47,
%T A331912 49,52,53,58,59,61,64,65,67,71,73,74,79,81,83,86,87,89,91,94,97,101,
%U A331912 103,104,107,109,111,113,116,117,121,122,125,127,128,129,131,137
%N A331912 Lexicographically earliest sequence of positive integers that have at most one distinct prime index already in the sequence.
%C A331912 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.
%C A331912 Conjecture: a(n)/A331784(n) -> 1 as n -> infinity.
%H A331912 Gus Wiseman, <a href="/A331912/a331912.png">Plot of A331912(n)/A331784(n) for n = 1..3729.</a>
%e A331912 The sequence of terms together with their prime indices begins:
%e A331912 1: {} 37: {12} 86: {1,14}
%e A331912 2: {1} 39: {2,6} 87: {2,10}
%e A331912 3: {2} 41: {13} 89: {24}
%e A331912 4: {1,1} 43: {14} 91: {4,6}
%e A331912 5: {3} 47: {15} 94: {1,15}
%e A331912 7: {4} 49: {4,4} 97: {25}
%e A331912 8: {1,1,1} 52: {1,1,6} 101: {26}
%e A331912 9: {2,2} 53: {16} 103: {27}
%e A331912 11: {5} 58: {1,10} 104: {1,1,1,6}
%e A331912 13: {6} 59: {17} 107: {28}
%e A331912 16: {1,1,1,1} 61: {18} 109: {29}
%e A331912 17: {7} 64: {1,1,1,1,1,1} 111: {2,12}
%e A331912 19: {8} 65: {3,6} 113: {30}
%e A331912 23: {9} 67: {19} 116: {1,1,10}
%e A331912 25: {3,3} 71: {20} 117: {2,2,6}
%e A331912 26: {1,6} 73: {21} 121: {5,5}
%e A331912 27: {2,2,2} 74: {1,12} 122: {1,18}
%e A331912 29: {10} 79: {22} 125: {3,3,3}
%e A331912 31: {11} 81: {2,2,2,2} 127: {31}
%e A331912 32: {1,1,1,1,1} 83: {23} 128: {1,1,1,1,1,1,1}
%e A331912 For example, the prime indices of 117 are {2,2,6}, of which only 2 is already in the sequence, so 117 is in the sequence.
%t A331912 aQ[n_]:=Length[Select[PrimePi/@First/@If[n==1,{},FactorInteger[n]],aQ]]<=1;
%t A331912 Select[Range[100],aQ]
%Y A331912 Contains all prime powers A000961.
%Y A331912 Numbers S without all prime indices in S are A324694.
%Y A331912 Numbers S without any prime indices in S are A324695.
%Y A331912 Numbers S with at most one prime index in S are A331784.
%Y A331912 Numbers S with exactly one prime index in S are A331785.
%Y A331912 Numbers S with exactly one distinct prime index in S are A331913.
%Y A331912 Cf. A000002, A000720, A001222, A001462, A324696, A331683, A331873, A331914.
%K A331912 nonn
%O A331912 1,2
%A A331912 _Gus Wiseman_, Feb 01 2020