This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102067 #23 Feb 16 2025 08:32:55
%S A102067 12,24,45,48,80,90,96,135,160,175,180,189,192,224,240,270,320,350,360,
%T A102067 378,384,405,448,480,525,539,540,567,637,640,672,700,720,756,768,810,
%U A102067 875,896,945,960,1050,1078,1080,1120,1134,1215,1274,1280,1344,1375,1400,1440
%N A102067 Numbers k such that k does not divide P(k)! even though P(k)^2 is not a factor of k, where P(k) is the largest prime factor of k.
%C A102067 Clearly, if P(k)^2 is a factor of k, then k does not divide P(k)!. Each member shows that the converse is false.
%C A102067 k is a member if and only if k is in A057109 but not in A070003.
%H A102067 Amiram Eldar, <a href="/A102067/b102067.txt">Table of n, a(n) for n = 1..10000</a>
%H A102067 Paul Erdős and Ilias Kastanas, <a href="http://www.jstor.org/stable/2324376">Solution 6674: The smallest factorial that is a multiple of n</a>, Amer. Math. Monthly, Vol. 101, No. 2 (1994), p. 179.
%H A102067 Aubrey J. Kempner, <a href="http://www.jstor.org/stable/2972639">Miscellanea</a>, Amer. Math. Monthly, Vol. 25, No. 5 (1918), pp. 201-210. See Section II, "Concerning the smallest integer m! divisible by a given integer n."
%H A102067 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>.
%H A102067 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%e A102067 12 does not divide P(12)! = 3! and 3^2 is not a factor of 12.
%t A102067 q[n_] := Module[{p = FactorInteger[n][[-1, 1]]}, !Divisible[n, p^2] && !Divisible[p!, n]]; Select[Range[1500], q] (* _Amiram Eldar_, Mar 30 2021 *)
%o A102067 (PARI) isok(n) = {my(f = factor(n)); my(P = f[#f~,1]); (P! % n) && (n % P^2);} \\ _Michel Marcus_, Sep 16 2015
%Y A102067 Cf. A006530, A057109, A070003, A102068.
%K A102067 nonn
%O A102067 1,1
%A A102067 _Jonathan Sondow_, Dec 28 2004
%E A102067 More terms from _Michel Marcus_, Sep 16 2015