A100717 - OEIS

%I #20 Jun 25 2022 08:24:45

%S 4,12,20,27,28,36,44,52,54,60,68,76,84,92,100,108,116,124,132,135,140,

%T 148,156,164,172,180,188,189,196,204,212,216,220,228,236,244,252,260,

%U 268,270,276,284,292,297,300,308,316,324,332,340,348,351,356,364,372

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

%C For each prime p, the sequence includes all k*p^p for k such that gcd(k,p)=1. - _T. D. Noe_

%C 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

%H Reinhard Zumkeller, <a href="/A100717/b100717.txt">Table of n, a(n) for n = 1..10000</a>

%F A203908(a(n)) = 0. - _Reinhard Zumkeller_, Dec 24 2013

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

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

%o (Haskell)

%o a100717 n = a100717_list !! (n-1)

%o a100717_list = filter ((== 0) . a203908) [1..]

%o -- _Reinhard Zumkeller_, Dec 24 2013

%Y Cf. A100716, A203908.

%Y Subsequences: A051674, A048102 \ {1}.

%K nonn

%O 1,1

%A _Leroy Quet_, Dec 10 2004

%E More terms from _T. D. Noe_ and _Robert G. Wilson v_, Dec 14 2004