A378158 Numbers k such that lpf(!k) < lpf(k-1), where lpf(k) = A020639(k) and !k = A000166(k).

20, 38, 42, 60, 90, 104, 108, 110, 114, 132, 138, 152, 164, 170, 174, 192, 194, 198, 240, 242, 258, 284, 294, 324, 338, 350, 360, 368, 390, 398, 434, 438, 450, 462, 482, 488, 500, 504, 510, 522, 524, 528, 542, 548, 564, 570, 588, 600, 602, 614, 618, 632, 642, 644, 648

Offset: 1

Author

Amiram Eldar, Nov 18 2024

Keywords

• nonn

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000166, A020639, A337986, A378157.

Programs

Mathematica

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]

PARI

ok(k, p) = {my(q = 2); while(q < p && k % q, q = nextprime(q+1)); q < p;}
lista(kmax) = {my(s = 1); for(k = 3, kmax, s = k * s + (-1)^k; if(ok(s, factor(k-1)[1,1]), print1(k, ", ")));}