login
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.
0
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
1,1
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, ...
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
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Sep 04 2021
EXTENSIONS
More terms from Amiram Eldar, Sep 04 2021
STATUS
approved