A100717 Numbers k having a prime divisor p such that p^p is the highest power of p that divides k.

4, 12, 20, 27, 28, 36, 44, 52, 54, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 135, 140, 148, 156, 164, 172, 180, 188, 189, 196, 204, 212, 216, 220, 228, 236, 244, 252, 260, 268, 270, 276, 284, 292, 297, 300, 308, 316, 324, 332, 340, 348, 351, 356, 364, 372

Offset: 1

Author

Leroy Quet, Dec 10 2004

Keywords

• nonn

Comments

For each prime p, the sequence includes all k*p^p for k such that gcd(k,p)=1. - T. D. Noe

The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 1/p^p + 1/p^(p+1)) = 0.14682429539560371215... . - Amiram Eldar, Jun 25 2022

Examples

			54 is included because 3^3, but not 3^4, divides 54.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A100716, A203908.

Subsequences: A051674, A048102 \ {1}.

Programs

Haskell

a100717 n = a100717_list !! (n-1)
a100717_list = filter ((== 0) . a203908) [1..]
-- Reinhard Zumkeller, Dec 24 2013

Mathematica

fQ[n_] := Union[ Table[ #[[1]] == #[[2]]] & /@ FactorInteger[n]][[ -1]] == True; Select[ Range[2, 375], fQ[ # ] &] (* Robert G. Wilson v, Dec 14 2004 *)

Formula

A203908(a(n)) = 0. - Reinhard Zumkeller, Dec 24 2013

Extensions

More terms from T. D. Noe and Robert G. Wilson v, Dec 14 2004