A362239 Primes such that all composite numbers up to the next prime have the same number of distinct prime divisors.

2, 3, 5, 11, 17, 19, 29, 37, 41, 43, 53, 59, 71, 97, 101, 107, 137, 149, 157, 179, 191, 197, 223, 227, 239, 269, 281, 311, 347, 419, 431, 461, 499, 521, 569, 599, 617, 641, 643, 659, 673, 739, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151

Offset: 1

Author

Mike Jones, Apr 12 2023

Keywords

• nonn

Examples

			19 is a term because 19 is a prime and each of the composite numbers up to the next prime (20, 21, and 22) has exactly 2 distinct prime divisors.
		

Crossrefs

A001359 is a subsequence.

Cf. A001221 (omega).

Programs

Mathematica

q[p_] := Length[Union[Table[PrimeNu[c], {c, Range[p + 1, NextPrime[p] - 1]}]]] <= 1; Select[Prime[Range[200]], q] (* Amiram Eldar, May 18 2023 *)

PARI

isok(p)=if(isprime(p), my(q=nextprime(p+1), t=omega(p+1)); for(i=p+2, q-1, if(omega(i)<>t, return(0))); 1, 0) \\ Andrew Howroyd, Apr 12 2023

Extensions

More terms from Andrew Howroyd, Apr 12 2023