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A331914
Numbers with at most one prime prime index, counted with multiplicity.
7
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, 32, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 52, 53, 56, 57, 58, 59, 61, 62, 64, 65, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 86, 87
OFFSET
1,2
COMMENTS
First differs from A324935 in having 39.
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: {} 24: {1,1,1,2} 52: {1,1,6}
2: {1} 26: {1,6} 53: {16}
3: {2} 28: {1,1,4} 56: {1,1,1,4}
4: {1,1} 29: {10} 57: {2,8}
5: {3} 31: {11} 58: {1,10}
6: {1,2} 32: {1,1,1,1,1} 59: {17}
7: {4} 34: {1,7} 61: {18}
8: {1,1,1} 35: {3,4} 62: {1,11}
10: {1,3} 37: {12} 64: {1,1,1,1,1,1}
11: {5} 38: {1,8} 65: {3,6}
12: {1,1,2} 39: {2,6} 67: {19}
13: {6} 40: {1,1,1,3} 68: {1,1,7}
14: {1,4} 41: {13} 69: {2,9}
16: {1,1,1,1} 42: {1,2,4} 70: {1,3,4}
17: {7} 43: {14} 71: {20}
19: {8} 44: {1,1,5} 73: {21}
20: {1,1,3} 46: {1,9} 74: {1,12}
21: {2,4} 47: {15} 76: {1,1,8}
22: {1,5} 48: {1,1,1,1,2} 77: {4,5}
23: {9} 49: {4,4} 78: {1,2,6}
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 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 exactly one prime prime index are A331915.
Numbers with exactly one distinct prime prime index are A331916.
Numbers with at most one distinct prime prime index are A331995.
Sequence in context: A210940 A257500 A121208 * A324935 A328369 A207674
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 08 2020
STATUS
approved