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