A357170 Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a prime power.

3, 5, 7, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 73, 79, 83, 89, 101, 103, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 181, 193, 199, 211, 223, 229, 233, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 349, 353, 359, 367, 373

Offset: 1

Author

Claude H. R. Dequatre, Sep 16 2022

Keywords

• nonn
• easy

Examples

			19 is a term because up to the next prime 23, tau(20) = 6, tau(21) = 4, tau(22) = 4, thus the smallest tau(k) is 4 and 4 is a prime power (2^2).
97 is prime but not a term because up to the next prime 101, tau(98) = 6, tau(99) = 6, tau(100) = 9, thus the smallest tau(k) is 6 and 6 is not a prime power.
		

Crossrefs

Cf. A000005, A000040, A061112, A246655.

Cf. A353284, A353285, A353286, A356833, A357175.

Programs

PARI

isok(p)=isprimepower(vecmin(apply(numdiv, [p+1..nextprime(p+1)-1])));
forprime(p=3, 2000, if(isok(p), print1(p", ")))