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A331916 Numbers with exactly one distinct prime prime index.

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%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