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

1,1

Links

Table of n, a(n) for n=1..55.

Example

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

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 *)

Prog

(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

Crossrefs

Intersection of A002808 and A335284.

Cf. A002110, A260188.

Sequence in context: A350061 A067893 A067794 * A068874 A018936 A212190

Adjacent sequences: A377881 A377882 A377883 * A377885 A377886 A377887

Keyword

nonn,new

Author

Daniel D Gibson, Nov 10 2024

Status

approved