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

1,1

Links

Table of n, a(n) for n=1..60.

Example

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.

Prog

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

Crossrefs

Cf. A000005, A000040, A061112, A246655.

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

Sequence in context: A077133 A164642 A247633 * A277717 A120460 A387591

Adjacent sequences: A357167 A357168 A357169 * A357171 A357172 A357173

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Sep 16 2022

Status

approved