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%I #8 Jun 10 2020 14:06:26
%S 1,2,3,4,5,6,7,8,10,11,12,13,14,16,17,19,20,21,22,23,24,26,28,29,31,
%T 32,34,35,37,38,39,40,41,42,43,44,46,47,48,49,52,53,56,57,58,59,61,62,
%U 64,65,67,68,69,70,71,73,74,76,77,78,79,80,82,83,84,86,87
%N Numbers with at most one prime prime index, counted with multiplicity.
%C First differs from A324935 in having 39.
%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: {} 24: {1,1,1,2} 52: {1,1,6}
%e 2: {1} 26: {1,6} 53: {16}
%e 3: {2} 28: {1,1,4} 56: {1,1,1,4}
%e 4: {1,1} 29: {10} 57: {2,8}
%e 5: {3} 31: {11} 58: {1,10}
%e 6: {1,2} 32: {1,1,1,1,1} 59: {17}
%e 7: {4} 34: {1,7} 61: {18}
%e 8: {1,1,1} 35: {3,4} 62: {1,11}
%e 10: {1,3} 37: {12} 64: {1,1,1,1,1,1}
%e 11: {5} 38: {1,8} 65: {3,6}
%e 12: {1,1,2} 39: {2,6} 67: {19}
%e 13: {6} 40: {1,1,1,3} 68: {1,1,7}
%e 14: {1,4} 41: {13} 69: {2,9}
%e 16: {1,1,1,1} 42: {1,2,4} 70: {1,3,4}
%e 17: {7} 43: {14} 71: {20}
%e 19: {8} 44: {1,1,5} 73: {21}
%e 20: {1,1,3} 46: {1,9} 74: {1,12}
%e 21: {2,4} 47: {15} 76: {1,1,8}
%e 22: {1,5} 48: {1,1,1,1,2} 77: {4,5}
%e 23: {9} 49: {4,4} 78: {1,2,6}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],Count[primeMS[#],_?PrimeQ]<=1&]
%Y These are numbers n such that A257994(n) <= 1.
%Y Prime-indexed primes are A006450, with products A076610.
%Y The number of distinct prime prime indices is A279952.
%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 exactly one prime prime index are A331915.
%Y Numbers with exactly one distinct prime prime index are A331916.
%Y Numbers with at most one distinct prime prime index are A331995.
%Y Cf. A000040, A000720, A007097, A018252, A112798, A320628, A330945, A331785.
%K nonn
%O 1,2
%A _Gus Wiseman_, Feb 08 2020
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