A331916 Numbers with exactly one distinct prime prime index.

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.

Links

Table of n, a(n) for n=1..62.

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.

Cf. A000040, A000720, A007097, A007821, A018252, A112798, A289509, A320628, A330944, A330945, A331784.

Sequence in context: A267312 A362579 A331386 * A371127 A269390 A056875

Adjacent sequences: A331913 A331914 A331915 * A331917 A331918 A331919

Keyword

nonn

Author

Gus Wiseman, Feb 08 2020

Status

approved