A377884 Composite numbers k without prime factors that are divisors of the greatest primorial less than k.

25, 49, 77, 91, 119, 121, 133, 143, 161, 169, 187, 203, 209, 221, 247, 253, 289, 299, 319, 323, 341, 361, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 529, 533, 551, 559, 583, 589, 611, 629, 649, 667, 671, 689, 697, 703, 713, 731, 737, 767, 779, 781, 793, 799

Offset: 1

Author

Daniel D Gibson, Nov 10 2024

Keywords

• nonn

Examples

			The greatest primorial below 25 is 6, the factors of which are 2 and 3, neither of which are factors of 25=5^2.
		

Crossrefs

Intersection of A002808 and A335284.

Cf. A002110, A260188.

Programs

Mathematica

q[k_] := Module[{p = 2, r = 2}, If[CompositeQ[k], While[r < k && ! Divisible[k, p], p = NextPrime[p]; r *= p]; r >= k, False]]; Select[Range[800], q] (* Amiram Eldar, Nov 14 2024 *)

PARI

P(n)=my(t=1, k); forprime(p=2, , k=t*p; if(k>n, return(t), t=k)); \\ A260188
isok(k) = (k>1) && !isprime(k) && (gcd(k, P(k-1)) == 1); \\ Michel Marcus, Nov 12 2024