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A331995
Numbers with at most one distinct prime prime index.
3
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, 28, 29, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 76
OFFSET
1,2
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:
1: {} 22: {1,5} 44: {1,1,5}
2: {1} 23: {9} 46: {1,9}
3: {2} 24: {1,1,1,2} 47: {15}
4: {1,1} 25: {3,3} 48: {1,1,1,1,2}
5: {3} 26: {1,6} 49: {4,4}
6: {1,2} 27: {2,2,2} 50: {1,3,3}
7: {4} 28: {1,1,4} 52: {1,1,6}
8: {1,1,1} 29: {10} 53: {16}
9: {2,2} 31: {11} 54: {1,2,2,2}
10: {1,3} 32: {1,1,1,1,1} 56: {1,1,1,4}
11: {5} 34: {1,7} 57: {2,8}
12: {1,1,2} 35: {3,4} 58: {1,10}
13: {6} 36: {1,1,2,2} 59: {17}
14: {1,4} 37: {12} 61: {18}
16: {1,1,1,1} 38: {1,8} 62: {1,11}
17: {7} 39: {2,6} 63: {2,2,4}
18: {1,2,2} 40: {1,1,1,3} 64: {1,1,1,1,1,1}
19: {8} 41: {13} 65: {3,6}
20: {1,1,3} 42: {1,2,4} 67: {19}
21: {2,4} 43: {14} 68: {1,1,7}
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.
Numbers whose prime indices are not all prime are A330945.
Numbers with at least one prime prime index are A331386.
The set S of numbers with at most one prime index in S are A331784.
The set S of numbers with at most one distinct prime index in S are A331912.
Numbers with at most one prime prime index are A331914.
Numbers with exactly one prime prime index are A331915.
Numbers with exactly one distinct prime prime index are A331916.
Sequence in context: A105427 A247160 A023808 * A347457 A318991 A322901
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 08 2020
STATUS
approved