A353939 Smallest b > 1 such that b^(p-1) == 1 (mod p^6) for p = prime(n).

65, 728, 1068, 34967, 284995, 861642, 390112, 333257, 2818778, 42137700, 8078311, 33518159, 92331463, 21583010, 138173066, 8202731, 390421192, 1006953931, 77622331, 270657300, 5915704483, 522911165, 2507851273, 1329885769, 2789067613, 3987072867, 7938255646

Offset: 1

Author

Felix Fröhlich, May 12 2022

Keywords

• nonn

Crossrefs

Row k = 6 of A257833.

Cf. similar sequences for p^k: A039678 (k=2), A249275 (k=3), A353937 (k=4), A353938 (k=5), A353940 (k=7), A353941 (k=8), A353942 (k=9), A353943 (k=10).

Programs

Mathematica

a[n_] := Module[{p = Prime[n], b = 2}, While[PowerMod[b, p - 1, p^6] != 1, b++]; b]; Array[a, 9] (* Amiram Eldar, May 12 2022 *)

PARI

a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^6)^(p-1)==1, return(b)))

Python

from sympy import prime
from sympy.ntheory.residue_ntheory import nthroot_mod
def A353939(n): return 2**6+1 if n == 1 else int(nthroot_mod(1,(p:= prime(n))-1,p**6,True)[1]) # Chai Wah Wu, May 17 2022

Extensions

a(25)-a(27) from Jinyuan Wang, May 17 2022