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A331916
Numbers with exactly one distinct prime prime index.
6
3, 5, 6, 9, 10, 11, 12, 17, 18, 20, 21, 22, 24, 25, 27, 31, 34, 35, 36, 39, 40, 41, 42, 44, 48, 50, 54, 57, 59, 62, 63, 65, 67, 68, 69, 70, 72, 77, 78, 80, 81, 82, 83, 84, 87, 88, 95, 96, 100, 108, 109, 111, 114, 115, 117, 118, 119, 121, 124, 125, 126, 127
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} 40: {1,1,1,3} 81: {2,2,2,2}
5: {3} 41: {13} 82: {1,13}
6: {1,2} 42: {1,2,4} 83: {23}
9: {2,2} 44: {1,1,5} 84: {1,1,2,4}
10: {1,3} 48: {1,1,1,1,2} 87: {2,10}
11: {5} 50: {1,3,3} 88: {1,1,1,5}
12: {1,1,2} 54: {1,2,2,2} 95: {3,8}
17: {7} 57: {2,8} 96: {1,1,1,1,1,2}
18: {1,2,2} 59: {17} 100: {1,1,3,3}
20: {1,1,3} 62: {1,11} 108: {1,1,2,2,2}
21: {2,4} 63: {2,2,4} 109: {29}
22: {1,5} 65: {3,6} 111: {2,12}
24: {1,1,1,2} 67: {19} 114: {1,2,8}
25: {3,3} 68: {1,1,7} 115: {3,9}
27: {2,2,2} 69: {2,9} 117: {2,2,6}
31: {11} 70: {1,3,4} 118: {1,17}
34: {1,7} 72: {1,1,1,2,2} 119: {4,7}
35: {3,4} 77: {4,5} 121: {5,5}
36: {1,1,2,2} 78: {1,2,6} 124: {1,1,11}
39: {2,6} 80: {1,1,1,1,3} 125: {3,3,3}
MATHEMATICA
Select[Range[100], Count[PrimePi/@First/@FactorInteger[#], _?PrimeQ]==1&]
CROSSREFS
These are numbers n such that A279952(n) = 1.
Prime-indexed primes are A006450, with products A076610.
The number of prime prime indices is A257994.
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 at most one distinct prime prime index are A331995.
Sequence in context: A267312 A362579 A331386 * A371127 A269390 A056875
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 08 2020
STATUS
approved