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A362239
Primes such that all composite numbers up to the next prime have the same number of distinct prime divisors.
0
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
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
KEYWORD
nonn
AUTHOR
Mike Jones, Apr 12 2023
EXTENSIONS
More terms from Andrew Howroyd, Apr 12 2023
STATUS
approved