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 A378158 #7 Nov 19 2024 00:59:04
%S A378158 20,38,42,60,90,104,108,110,114,132,138,152,164,170,174,192,194,198,
%T A378158 240,242,258,284,294,324,338,350,360,368,390,398,434,438,450,462,482,
%U A378158 488,500,504,510,522,524,528,542,548,564,570,588,600,602,614,618,632,642,644,648
%N A378158 Numbers k such that lpf(!k) < lpf(k-1), where lpf(k) = A020639(k) and !k = A000166(k).
%C A378158 Since (k-1) | !k, we have lpf(!k) <= lpf(k-1). This sequence gives the values of k for which the inequality holds.
%H A378158 Amiram Eldar, <a href="/A378158/b378158.txt">Table of n, a(n) for n = 1..10000</a>
%t A378158 okQ[k_, p_] := Module[{q = 2}, While[q < p && !Divisible[k, q], q = NextPrime[q]]; q < p]; q[k_] := okQ[Subfactorial[k], FactorInteger[k-1][[1, 1]]]; Select[Range[3, 650], q]
%o A378158 (PARI) ok(k, p) = {my(q = 2); while(q < p && k % q, q = nextprime(q+1)); q < p;}
%o A378158 lista(kmax) = {my(s = 1); for(k = 3, kmax, s = k * s + (-1)^k; if(ok(s, factor(k-1)[1,1]), print1(k, ", ")));}
%Y A378158 Cf. A000166, A020639, A337986, A378157.
%K A378158 nonn
%O A378158 1,1
%A A378158 _Amiram Eldar_, Nov 18 2024