A378158 - OEIS

%I #7 Nov 19 2024 00:59:04

%S 20,38,42,60,90,104,108,110,114,132,138,152,164,170,174,192,194,198,

%T 240,242,258,284,294,324,338,350,360,368,390,398,434,438,450,462,482,

%U 488,500,504,510,522,524,528,542,548,564,570,588,600,602,614,618,632,642,644,648

%N Numbers k such that lpf(!k) < lpf(k-1), where lpf(k) = A020639(k) and !k = A000166(k).

%C Since (k-1) | !k, we have lpf(!k) <= lpf(k-1). This sequence gives the values of k for which the inequality holds.

%H Amiram Eldar, <a href="/A378158/b378158.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 (PARI) ok(k, p) = {my(q = 2); while(q < p && k % q, q = nextprime(q+1)); q < p;}

%o 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 Cf. A000166, A020639, A337986, A378157.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 18 2024