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A100717
Numbers k having a prime divisor p such that p^p is the highest power of p that divides k.
8
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
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
Subsequences: A051674, A048102 \ {1}.
Sequence in context: A273541 A273215 A273277 * A365883 A285526 A321466
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