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%I #6 Feb 08 2020 08:16:09
%S 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 28,29,31,32,34,35,36,37,38,39,40,41,42,43,44,46,47,48,49,50,52,53,54,
%U 56,57,58,59,61,62,63,64,65,67,68,69,70,71,72,73,74,76
%N Numbers with at most 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 1: {} 22: {1,5} 44: {1,1,5}
%e 2: {1} 23: {9} 46: {1,9}
%e 3: {2} 24: {1,1,1,2} 47: {15}
%e 4: {1,1} 25: {3,3} 48: {1,1,1,1,2}
%e 5: {3} 26: {1,6} 49: {4,4}
%e 6: {1,2} 27: {2,2,2} 50: {1,3,3}
%e 7: {4} 28: {1,1,4} 52: {1,1,6}
%e 8: {1,1,1} 29: {10} 53: {16}
%e 9: {2,2} 31: {11} 54: {1,2,2,2}
%e 10: {1,3} 32: {1,1,1,1,1} 56: {1,1,1,4}
%e 11: {5} 34: {1,7} 57: {2,8}
%e 12: {1,1,2} 35: {3,4} 58: {1,10}
%e 13: {6} 36: {1,1,2,2} 59: {17}
%e 14: {1,4} 37: {12} 61: {18}
%e 16: {1,1,1,1} 38: {1,8} 62: {1,11}
%e 17: {7} 39: {2,6} 63: {2,2,4}
%e 18: {1,2,2} 40: {1,1,1,3} 64: {1,1,1,1,1,1}
%e 19: {8} 41: {13} 65: {3,6}
%e 20: {1,1,3} 42: {1,2,4} 67: {19}
%e 21: {2,4} 43: {14} 68: {1,1,7}
%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 Numbers whose prime indices are not all prime are A330945.
%Y Numbers with at least one prime prime index are A331386.
%Y The set S of numbers with at most one prime index in S are A331784.
%Y The set S of numbers with at most one distinct prime index in S are A331912.
%Y Numbers with at most one prime prime index are A331914.
%Y Numbers with exactly one prime prime index are A331915.
%Y Numbers with exactly one distinct prime prime index are A331916.
%Y Cf. A000040, A000720, A001221, A007097, A007821, A112798, A257994, A320628, A330944, A331785, A331912, A331913.
%K nonn
%O 1,2
%A _Gus Wiseman_, Feb 08 2020