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A331915
Numbers with exactly one prime prime index, counted with multiplicity.
5
3, 5, 6, 10, 11, 12, 17, 20, 21, 22, 24, 31, 34, 35, 39, 40, 41, 42, 44, 48, 57, 59, 62, 65, 67, 68, 69, 70, 77, 78, 80, 82, 83, 84, 87, 88, 95, 96, 109, 111, 114, 115, 118, 119, 124, 127, 129, 130, 134, 136, 138, 140, 141, 143, 145, 147, 154, 156, 157, 159
OFFSET
1,1
COMMENTS
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.
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2} 57: {2,8} 114: {1,2,8}
5: {3} 59: {17} 115: {3,9}
6: {1,2} 62: {1,11} 118: {1,17}
10: {1,3} 65: {3,6} 119: {4,7}
11: {5} 67: {19} 124: {1,1,11}
12: {1,1,2} 68: {1,1,7} 127: {31}
17: {7} 69: {2,9} 129: {2,14}
20: {1,1,3} 70: {1,3,4} 130: {1,3,6}
21: {2,4} 77: {4,5} 134: {1,19}
22: {1,5} 78: {1,2,6} 136: {1,1,1,7}
24: {1,1,1,2} 80: {1,1,1,1,3} 138: {1,2,9}
31: {11} 82: {1,13} 140: {1,1,3,4}
34: {1,7} 83: {23} 141: {2,15}
35: {3,4} 84: {1,1,2,4} 143: {5,6}
39: {2,6} 87: {2,10} 145: {3,10}
40: {1,1,1,3} 88: {1,1,1,5} 147: {2,4,4}
41: {13} 95: {3,8} 154: {1,4,5}
42: {1,2,4} 96: {1,1,1,1,1,2} 156: {1,1,2,6}
44: {1,1,5} 109: {29} 157: {37}
48: {1,1,1,1,2} 111: {2,12} 159: {2,16}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Count[primeMS[#], _?PrimeQ]==1&]
CROSSREFS
These are numbers n such that A257994(n) = 1.
Prime-indexed primes are A006450, with products A076610.
The number of distinct prime prime indices is A279952.
Numbers with at least one prime prime index are A331386.
The set S of numbers with exactly one prime index in S are A331785.
The set S of numbers with exactly one distinct prime index in S are A331913.
Numbers with at most one prime prime index are A331914.
Numbers with exactly one distinct prime prime index are A331916.
Numbers with at most one distinct prime prime index are A331995.
Sequence in context: A244671 A232531 A182637 * A065512 A066147 A175304
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 08 2020
STATUS
approved