A169980 - OEIS

%I #16 Jan 28 2019 23:50:41

%S 0,1,29,1,29,5,2039,1,463,775,289,17,2039,1,811,12899,463,1,1280537,1,

%T 11519,1,637,41,31933,5,1507,775,811,53,34488049,1,463,62483,29,289,

%U 91560011,1,29,37,182293,77,2346073,1,56003,230759,1333,1,3051091,1,28859,61,1507

%N Numerator(Bernoulli(2n)) mod denominator(Bernoulli(2n)).

%C From _Robert G. Wilson v_, Aug 27 2010: (Start)

%C From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.

%C Values sorted: 1, 5, 17, 29, 37, 41, 49, 53, 61, 65, 77, 101, 137, 161, 169, 173, 181, 185, 221, 229, ..., .

%C a(n)== 1 for n's: 1, 3, 7, 13, 17, 19, 21, 31, 37, 43, 47, 49, 57, 59, 61, 67, 71, 73, 79, 91, 93, 97, ..., .

%C a(n)== 5 for n's: 5, 25, 85, 185, 235, 295, 305, 335, 355, 365, 395, 425, 505, 535, 635, 685, 695, ..., . A051229

%C a(n)==17 for n's: 11, 77, 87, 121, 143, 187, 407, 517, 539, 649, 671, 737, 781, 847, 869, 1067, 1111, ..., .

%C a(n)==29 for n's: 2, 4, 34, 38, 62, 76, 94, 118, 122, 124, 142, 188, 202, 206, 214, 218, 236, 244, ..., . A051225

%C a(n)==37 for n's: 39, 507, 1209, 1677, 3783, 4251, 5421, 5811, 6123, 6357, 6513, 7526, 7682, 7760, 8228, ..., .

%C a(n)==41 for n's: 23, 123, 161, 391, 437, 529, 851, 1081, 1127, 1357, 1403, 1633, 1817, 2323, 2369, 2461, ..., .

%C a(n)==49 for n's: 55, 275, 605, 2035, 3025, 3355, 3685, 3905, 4345, 5555, 5885, 6985, 7535, 7645, 8195, ..., .

%C a(n)==53 for n's: 29, 203, 377, 493, 841, 899, 1073, 1247, 1363, 1711, 1943, 2059, 2117, 2813, 2929, 2987, ..., .

%C a(n)==61 for n's: 51, 867, 2193, 3009, 3417, 6477, 7089, 8007, 8313, 8517, 10047, 10149, 11577, 11679, ..., .

%C a(n)==65 for n's: 159, 6837, 8427, 9381, 11289, 12561, 15423, 17331, 23691, 25917, 26553, 30687, 31323, ..., .

%C a(n)==77 for n's: 41, 287, 533, 697, 1517, 1681, 1927, 2419, 2747, 2911, 3239, 3731, 3977, 4141, 4387, ..., .

%C (End)

%H Robert G. Wilson v, <a href="/A169980/b169980.txt">Table of n, a(n) for n = 0..50000</a>.

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a> [From _Robert G. Wilson v_, Aug 27 2010]

%F A000367(n) mod A002445(n). [_Robert G. Wilson v_, Aug 27 2010]

%t f[n_] := Block[{b = BernoulliB[2 n]}, Mod[Numerator@b, Denominator@b]]; Array[f, 53, 0] (* _Robert G. Wilson v_, Aug 27 2010 *)

%o (PARI) a(n) = my(b = bernfrac(2*n)); numerator(b) % denominator(b); \\ _Michel Marcus_, Mar 15 2015

%Y Cf. A000367, A002445, A180315. [_Robert G. Wilson v_, Aug 27 2010]

%K nonn

%O 0,3

%A _Robert G. Wilson v_, Aug 19 2010