A331995 Numbers with at most one distinct prime prime index.

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

Author

Gus Wiseman, Feb 08 2020

Keywords

• nonn

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.

Examples

			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}
		

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.

Cf. A000040, A000720, A001221, A007097, A007821, A112798, A257994, A320628, A330944, A331785, A331912, A331913.

Programs

Mathematica

Select[Range[100],Count[PrimePi/@First/@FactorInteger[#],_?PrimeQ]<=1&]