cp's OEIS Frontend

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

%I A100717 #20 Jun 25 2022 08:24:45
%S A100717 4,12,20,27,28,36,44,52,54,60,68,76,84,92,100,108,116,124,132,135,140,
%T A100717 148,156,164,172,180,188,189,196,204,212,216,220,228,236,244,252,260,
%U A100717 268,270,276,284,292,297,300,308,316,324,332,340,348,351,356,364,372
%N A100717 Numbers k having a prime divisor p such that p^p is the highest power of p that divides k.
%C A100717 For each prime p, the sequence includes all k*p^p for k such that gcd(k,p)=1. - _T. D. Noe_
%C A100717 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 A100717 Reinhard Zumkeller, <a href="/A100717/b100717.txt">Table of n, a(n) for n = 1..10000</a>
%F A100717 A203908(a(n)) = 0. - _Reinhard Zumkeller_, Dec 24 2013
%e A100717 54 is included because 3^3, but not 3^4, divides 54.
%t A100717 fQ[n_] := Union[ Table[ #[[1]] == #[[2]]] & /@ FactorInteger[n]][[ -1]] == True; Select[ Range[2, 375], fQ[ # ] &] (* _Robert G. Wilson v_, Dec 14 2004 *)
%o A100717 (Haskell)
%o A100717 a100717 n = a100717_list !! (n-1)
%o A100717 a100717_list = filter ((== 0) . a203908) [1..]
%o A100717 -- _Reinhard Zumkeller_, Dec 24 2013
%Y A100717 Cf. A100716, A203908.
%Y A100717 Subsequences: A051674, A048102 \ {1}.
%K A100717 nonn
%O A100717 1,1
%A A100717 _Leroy Quet_, Dec 10 2004
%E A100717 More terms from _T. D. Noe_ and _Robert G. Wilson v_, Dec 14 2004