A356833 Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a square.

5, 13, 19, 31, 37, 43, 53, 61, 67, 73, 79, 83, 89, 103, 109, 127, 131, 139, 151, 157, 163, 173, 181, 193, 199, 211, 223, 233, 241, 251, 257, 263, 269, 271, 277, 293, 307, 311, 313, 317, 331, 337, 353, 367, 373, 379, 383, 389, 397, 401, 409, 421, 433, 443, 449, 457, 461, 463, 467, 479

Offset

1,1

Links

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

Example

13 is a term because up to the next prime 17, tau(14) = 4, tau(15) = 4, tau(16) = 5, thus the smallest tau(k) is 4 and 4 is a square (2^2).
23 is prime but not a term because up to the next prime 29, tau(24) = 8, tau(25) = 3, tau(26) = 4, tau(27) = 4, tau(28) = 6, thus the smallest tau(k) = 3 and 3 is not a square.

Prog

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

Crossrefs

Cf. A000005, A000040, A000290, A061112, A036436.

Cf. A353284, A353285, A353286, A357170, A357175.

Sequence in context: A129919 A045454 A377178 * A166575 A265808 A265790

Adjacent sequences: A356830 A356831 A356832 * A356834 A356835 A356836

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Sep 16 2022

Status

approved