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

1,1

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A100716, A203908.

Subsequences: A051674, A048102 \ {1}.

Sequence in context: A273541 A273215 A273277 * A365883 A285526 A321466

Adjacent sequences: A100714 A100715 A100716 * A100718 A100719 A100720

Keyword

nonn

Author

Leroy Quet, Dec 10 2004

Extensions

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

Status

approved