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Smallest b > 1 such that b^(p-1) == 1 (mod p^4) for p = prime(n).
8

%I #13 May 18 2022 07:54:58

%S 17,80,182,1047,1963,239,4260,2819,19214,2463,15714,51344,20677,3038,

%T 224444,189323,11550,397575,201305,15384,840838,1372873,1576656,

%U 278454,1721322,48072,281007,119551,252595,1001934,3489507,2489004,598987,3082551,6136759,3928984

%N Smallest b > 1 such that b^(p-1) == 1 (mod p^4) for p = prime(n).

%t a[n_] := Module[{p = Prime[n], b = 2}, While[PowerMod[b, p - 1, p^4] != 1, b++]; b]; Array[a, 20] (* _Amiram Eldar_, May 12 2022 *)

%o (PARI) a(n) = my(p=prime(n)); for(b=2, oo, if(Mod(b, p^4)^(p-1)==1, return(b)))

%o (Python)

%o from sympy import prime

%o from sympy.ntheory.residue_ntheory import nthroot_mod

%o def A353937(n): return 2**4+1 if n == 1 else int(nthroot_mod(1,(p:= prime(n))-1,p**4,True)[1]) # _Chai Wah Wu_, May 17 2022

%Y Row k = 4 of A257833.

%Y Cf. similar sequences for p^k: A039678 (k=2), A249275 (k=3), A353938 (k=5), A353939 (k=6), A353940 (k=7), A353941 (k=8), A353942 (k=9), A353943 (k=10).

%K nonn

%O 1,1

%A _Felix Fröhlich_, May 12 2022