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

1,1

Links

Table of n, a(n) for n=1..53.

Example

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.

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 *)

Prog

(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

Crossrefs

A001359 is a subsequence.

Cf. A001221 (omega).

Sequence in context: A040083 A045308 A245639 * A147813 A338578 A274386

Adjacent sequences: A362236 A362237 A362238 * A362240 A362241 A362242

Keyword

nonn

Author

Mike Jones, Apr 12 2023

Extensions

More terms from Andrew Howroyd, Apr 12 2023

Status

approved