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 A331916 #6 Feb 08 2020 08:15:53 %S A331916 3,5,6,9,10,11,12,17,18,20,21,22,24,25,27,31,34,35,36,39,40,41,42,44, %T A331916 48,50,54,57,59,62,63,65,67,68,69,70,72,77,78,80,81,82,83,84,87,88,95, %U A331916 96,100,108,109,111,114,115,117,118,119,121,124,125,126,127 %N A331916 Numbers with exactly one distinct prime prime index. %C A331916 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 A331916 The sequence of terms together with their prime indices begins: %e A331916 3: {2} 40: {1,1,1,3} 81: {2,2,2,2} %e A331916 5: {3} 41: {13} 82: {1,13} %e A331916 6: {1,2} 42: {1,2,4} 83: {23} %e A331916 9: {2,2} 44: {1,1,5} 84: {1,1,2,4} %e A331916 10: {1,3} 48: {1,1,1,1,2} 87: {2,10} %e A331916 11: {5} 50: {1,3,3} 88: {1,1,1,5} %e A331916 12: {1,1,2} 54: {1,2,2,2} 95: {3,8} %e A331916 17: {7} 57: {2,8} 96: {1,1,1,1,1,2} %e A331916 18: {1,2,2} 59: {17} 100: {1,1,3,3} %e A331916 20: {1,1,3} 62: {1,11} 108: {1,1,2,2,2} %e A331916 21: {2,4} 63: {2,2,4} 109: {29} %e A331916 22: {1,5} 65: {3,6} 111: {2,12} %e A331916 24: {1,1,1,2} 67: {19} 114: {1,2,8} %e A331916 25: {3,3} 68: {1,1,7} 115: {3,9} %e A331916 27: {2,2,2} 69: {2,9} 117: {2,2,6} %e A331916 31: {11} 70: {1,3,4} 118: {1,17} %e A331916 34: {1,7} 72: {1,1,1,2,2} 119: {4,7} %e A331916 35: {3,4} 77: {4,5} 121: {5,5} %e A331916 36: {1,1,2,2} 78: {1,2,6} 124: {1,1,11} %e A331916 39: {2,6} 80: {1,1,1,1,3} 125: {3,3,3} %t A331916 Select[Range[100],Count[PrimePi/@First/@FactorInteger[#],_?PrimeQ]==1&] %Y A331916 These are numbers n such that A279952(n) = 1. %Y A331916 Prime-indexed primes are A006450, with products A076610. %Y A331916 The number of prime prime indices is A257994. %Y A331916 Numbers with at least one prime prime index are A331386. %Y A331916 The set S of numbers with exactly one prime index in S are A331785. %Y A331916 The set S of numbers with exactly one distinct prime index in S are A331913. %Y A331916 Numbers with at most one prime prime index are A331914. %Y A331916 Numbers with at most one distinct prime prime index are A331995. %Y A331916 Cf. A000040, A000720, A007097, A007821, A018252, A112798, A289509, A320628, A330944, A330945, A331784. %K A331916 nonn %O A331916 1,1 %A A331916 _Gus Wiseman_, Feb 08 2020