A345675 - OEIS

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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

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OFFSET

1,1

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, ...

LINKS

Table of n, a(n) for n=1..28.

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 *)

PROG

(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

CROSSREFS

Cf. A027642, A105222, A121707, A316940.

Sequence in context: A271071 A249889 A030261 * A007102 A196542 A271072

Adjacent sequences: A345672 A345673 A345674 * A345676 A345677 A345678

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Sep 04 2021

EXTENSIONS

More terms from Amiram Eldar, Sep 04 2021

STATUS

approved