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A331995 Numbers with at most one distinct prime prime index.

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%I A331995 #6 Feb 08 2020 08:16:09
%S A331995 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,
%T A331995 28,29,31,32,34,35,36,37,38,39,40,41,42,43,44,46,47,48,49,50,52,53,54,
%U A331995 56,57,58,59,61,62,63,64,65,67,68,69,70,71,72,73,74,76
%N A331995 Numbers with at most one distinct prime prime index.
%C A331995 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 A331995 The sequence of terms together with their prime indices begins:
%e A331995    1: {}           22: {1,5}          44: {1,1,5}
%e A331995    2: {1}          23: {9}            46: {1,9}
%e A331995    3: {2}          24: {1,1,1,2}      47: {15}
%e A331995    4: {1,1}        25: {3,3}          48: {1,1,1,1,2}
%e A331995    5: {3}          26: {1,6}          49: {4,4}
%e A331995    6: {1,2}        27: {2,2,2}        50: {1,3,3}
%e A331995    7: {4}          28: {1,1,4}        52: {1,1,6}
%e A331995    8: {1,1,1}      29: {10}           53: {16}
%e A331995    9: {2,2}        31: {11}           54: {1,2,2,2}
%e A331995   10: {1,3}        32: {1,1,1,1,1}    56: {1,1,1,4}
%e A331995   11: {5}          34: {1,7}          57: {2,8}
%e A331995   12: {1,1,2}      35: {3,4}          58: {1,10}
%e A331995   13: {6}          36: {1,1,2,2}      59: {17}
%e A331995   14: {1,4}        37: {12}           61: {18}
%e A331995   16: {1,1,1,1}    38: {1,8}          62: {1,11}
%e A331995   17: {7}          39: {2,6}          63: {2,2,4}
%e A331995   18: {1,2,2}      40: {1,1,1,3}      64: {1,1,1,1,1,1}
%e A331995   19: {8}          41: {13}           65: {3,6}
%e A331995   20: {1,1,3}      42: {1,2,4}        67: {19}
%e A331995   21: {2,4}        43: {14}           68: {1,1,7}
%t A331995 Select[Range[100],Count[PrimePi/@First/@FactorInteger[#],_?PrimeQ]<=1&]
%Y A331995 These are numbers n such that A279952(n) <= 1.
%Y A331995 Prime-indexed primes are A006450, with products A076610.
%Y A331995 Numbers whose prime indices are not all prime are A330945.
%Y A331995 Numbers with at least one prime prime index are A331386.
%Y A331995 The set S of numbers with at most one prime index in S are A331784.
%Y A331995 The set S of numbers with at most one distinct prime index in S are A331912.
%Y A331995 Numbers with at most one prime prime index are A331914.
%Y A331995 Numbers with exactly one prime prime index are A331915.
%Y A331995 Numbers with exactly one distinct prime prime index are A331916.
%Y A331995 Cf. A000040, A000720, A001221, A007097, A007821, A112798, A257994, A320628, A330944, A331785, A331912, A331913.
%K A331995 nonn
%O A331995 1,2
%A A331995 _Gus Wiseman_, Feb 08 2020