A345675 Numbers m such that D_{m-1} is the smallest base b > 1 for which b^{m-1} == 1 (mod m), where D_k is the denominator (A027642) of Bernoulli number B_k.

35, 14315, 22399, 35711, 455891, 881809, 1198159, 1917071, 2287987, 3310037, 4464941, 11029439, 12190061, 13325753, 17832803, 33012941, 33296147, 37814849, 44986423, 74437181, 76911149, 82873661, 91909571, 98859851, 108266171, 128008159, 128981243, 132391409

Offset: 1

Author

Thomas Ordowski, Sep 04 2021

Keywords

• nonn

Comments

These are numbers m such that A027642(m-1) = A105222(m).

The corresponding bases of these pseudoprimes are 6, 6, 42, 66, 66, 46410, 3318, 66, 42, 30, 330, 6, 330, 61410, 6, 330, 1074, 510, 3318, 330, 7890, 330, 66, 12606, 66, 42, 6, 510, ...

Crossrefs

Cf. A027642, A105222, A121707, A316940.

Programs

Mathematica

Den[n_] := Times @@ (1 + Select[Divisors[n], PrimeQ[# + 1] &]); q[k_] := Module[{m = 2, d = Den[k - 1]}, If[PowerMod[d, k - 1, k] != 1, False, While[m < d && PowerMod[m, k - 1, k] != 1, m++]; m == d]]; Select[Range[3, 10^6, 2], q] (* Amiram Eldar, Sep 04 2021 *)

PARI

f(n) = my(m=2); while(Mod(m, n)^(n-1)!=1, m++); m;
isok(m) = f(m) == denominator(bernfrac(m-1)); \\ Michel Marcus, Sep 04 2021

Extensions

More terms from Amiram Eldar, Sep 04 2021