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 A331915 #5 Feb 08 2020 08:15:46 %S A331915 3,5,6,10,11,12,17,20,21,22,24,31,34,35,39,40,41,42,44,48,57,59,62,65, %T A331915 67,68,69,70,77,78,80,82,83,84,87,88,95,96,109,111,114,115,118,119, %U A331915 124,127,129,130,134,136,138,140,141,143,145,147,154,156,157,159 %N A331915 Numbers with exactly one prime prime index, counted with multiplicity. %C A331915 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. %e A331915 The sequence of terms together with their prime indices begins: %e A331915 3: {2} 57: {2,8} 114: {1,2,8} %e A331915 5: {3} 59: {17} 115: {3,9} %e A331915 6: {1,2} 62: {1,11} 118: {1,17} %e A331915 10: {1,3} 65: {3,6} 119: {4,7} %e A331915 11: {5} 67: {19} 124: {1,1,11} %e A331915 12: {1,1,2} 68: {1,1,7} 127: {31} %e A331915 17: {7} 69: {2,9} 129: {2,14} %e A331915 20: {1,1,3} 70: {1,3,4} 130: {1,3,6} %e A331915 21: {2,4} 77: {4,5} 134: {1,19} %e A331915 22: {1,5} 78: {1,2,6} 136: {1,1,1,7} %e A331915 24: {1,1,1,2} 80: {1,1,1,1,3} 138: {1,2,9} %e A331915 31: {11} 82: {1,13} 140: {1,1,3,4} %e A331915 34: {1,7} 83: {23} 141: {2,15} %e A331915 35: {3,4} 84: {1,1,2,4} 143: {5,6} %e A331915 39: {2,6} 87: {2,10} 145: {3,10} %e A331915 40: {1,1,1,3} 88: {1,1,1,5} 147: {2,4,4} %e A331915 41: {13} 95: {3,8} 154: {1,4,5} %e A331915 42: {1,2,4} 96: {1,1,1,1,1,2} 156: {1,1,2,6} %e A331915 44: {1,1,5} 109: {29} 157: {37} %e A331915 48: {1,1,1,1,2} 111: {2,12} 159: {2,16} %t A331915 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]; %t A331915 Select[Range[100],Count[primeMS[#],_?PrimeQ]==1&] %Y A331915 These are numbers n such that A257994(n) = 1. %Y A331915 Prime-indexed primes are A006450, with products A076610. %Y A331915 The number of distinct prime prime indices is A279952. %Y A331915 Numbers with at least one prime prime index are A331386. %Y A331915 The set S of numbers with exactly one prime index in S are A331785. %Y A331915 The set S of numbers with exactly one distinct prime index in S are A331913. %Y A331915 Numbers with at most one prime prime index are A331914. %Y A331915 Numbers with exactly one distinct prime prime index are A331916. %Y A331915 Numbers with at most one distinct prime prime index are A331995. %Y A331915 Cf. A000040, A000720, A007097, A007821, A018252, A112798, A289509, A320628, A330944, A330945, A331784. %K A331915 nonn %O A331915 1,1 %A A331915 _Gus Wiseman_, Feb 08 2020