A074661 Let n = 2^e_2 * 3^e_3 * 5^e_5 * ... be the prime factorization of n; sequence gives n such that max{e_2, e_3, ...} is prime.

4, 8, 9, 12, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 49, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 84, 88, 90, 92, 96, 98, 99, 100, 104, 108, 116, 117, 120, 121, 124, 125, 126, 128, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 164, 168, 169, 171, 172, 175, 180, 184

Offset: 1

Author

N. J. A. Sloane, Sep 18 2008

Keywords

• nonn

Comments

The old entry with this sequence number was a duplicate of A056594.

The largest exponent of the prime factors of n is prime. - Harvey P. Dale, Mar 09 2012

The asymptotic density of this sequence is Sum_{p prime} (1/zeta(p+1) - 1/zeta(p)) = 0.3391101054... - Amiram Eldar, Oct 18 2020

Links

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

Crossrefs

Cf. A096432, A060476.

Programs

Mathematica

Select[Range[200],PrimeQ[Max[Transpose[FactorInteger[#]][[2]]]]&] (* Harvey P. Dale, Mar 09 2012 *)

PARI

isA074661(n) = if(n<4,0,isprime(vecmax(factor(n)[,2])))