A331386 Numbers with at least one prime prime index.

3, 5, 6, 9, 10, 11, 12, 15, 17, 18, 20, 21, 22, 24, 25, 27, 30, 31, 33, 34, 35, 36, 39, 40, 41, 42, 44, 45, 48, 50, 51, 54, 55, 57, 59, 60, 62, 63, 65, 66, 67, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 83, 84, 85, 87, 88, 90, 93, 95, 96, 99, 100, 102, 105, 108

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.

The asymptotic density of this sequence is 1 - Product_{p in A006450} (1 - 1/p) = 1 - 1/(Sum_{n>=1} 1/A076610(n)) > 2/3. - Amiram Eldar, Feb 02 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

A257994(a(n)) > 0.

Example

The sequence of terms together with their prime indices begins:
    3: {2}
    5: {3}
    6: {1,2}
    9: {2,2}
   10: {1,3}
   11: {5}
   12: {1,1,2}
   15: {2,3}
   17: {7}
   18: {1,2,2}
   20: {1,1,3}
   21: {2,4}
   22: {1,5}
   24: {1,1,1,2}
   25: {3,3}
   27: {2,2,2}
   30: {1,2,3}
   31: {11}
   33: {2,5}
   34: {1,7}

Mathematica

Select[Range[100], MemberQ[FactorInteger[#], {_?(PrimeQ@*PrimePi), _}]&]

Crossrefs

Complement of A320628.

Positions of terms > 0 in A257994.

Positions of terms > 1 in A295665.

Primes of prime index are A006450.

Primes of nonprime index are A007821.

Products of primes of prime index are A076610.

Products of primes of nonprime index are A320628.

The number of nonprime prime indices is given by A330944.

Cf. A000040, A000720, A001222, A018252, A056239, A076610, A112798, A302242, A320633, A330943, A330944, A330947, A330949.

Sequence in context: A161182 A267312 A362579 * A331916 A371127 A269390

Adjacent sequences: A331383 A331384 A331385 * A331387 A331388 A331389

Keyword

nonn

Author

Gus Wiseman, Jan 17 2020

Status

approved