A355658 Smallest prime base q such that q^(p-1) == 1 (mod p^2), where p = prime(n).

5, 17, 7, 19, 3, 19, 131, 127, 263, 41, 229, 691, 313, 19, 53, 521, 53, 601, 1301, 11, 619, 31, 269, 3187, 53, 181, 43, 317, 499, 373, 911, 659, 19, 3659, 313, 751, 233, 4373, 3307, 419, 2591, 313, 1249, 2897, 349, 709, 331, 1973, 1933, 503, 821, 977, 2371, 263

Offset: 1

Author

Felix Fröhlich, Jul 12 2022

Keywords

• nonn

Comments

a(n) differs from A125636(n) if and only if p is a Wieferich prime (A001220). In particular, a(183) = 2 and A125636(183) = 18979. Similarly, a(490) = 2 and A125636(490) = 82183.

Crossrefs

Cf. A001220, A125636, A039678.

Programs

PARI

a(n) = my(p=prime(n)); forprime(q=1, , if(Mod(q, p^2)^(p-1)==1, return(q)))