A180315 AbsoluteValue(Numerator(Bernoulli(2n))) mod denominator(Bernoulli(2n)).

0, 1, 1, 1, 1, 5, 691, 1, 47, 775, 41, 17, 691, 1, 59, 12899, 47, 1, 638653, 1, 2011, 1, 53, 41, 14477, 5, 83, 775, 59, 53, 22298681, 1, 47, 62483, 1, 289, 48540859, 1, 1, 37, 47717, 77, 1058237, 1, 5407, 230759, 77, 1, 1450679, 1, 4471, 61, 83, 101, 71532367

Offset: 0

Author

Robert G. Wilson v, Aug 27 2010

Keywords

• nonn

Comments

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

Values sorted: 1, 5, 17, 37, 41, 47, 49, 53, 59, 61, 65, 77, 83, 89, 101, 113, 137, 161, 167, 169, 173, ..., .

a(n).==1 for n's: 1, 2, 3, 4, 7, 13, 17, 19, 21, 31, 34, 37, 38, 43, 47, 49, 57, 59, 61, 62, 67, 71, 73, ..., .

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

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

a(n)==37 for n's: 39, 507, 1209, 1677, 3783, 4251, 5421, 5811, 6123, 6357, 6513, 7527, 7683, 7761, 8229, ..., .

a(n)==41 for n's: 10, 23, 123, 161, 170, 391, 437, 529, 610, 710, 851, 1010, 1081, 1127, 1357, 1403, ..., .

a(n)==47 for n's: 8, 16, 32, 64, 152, 248, 304, 376, 472, 496, 752, 824, 872, 992, 1256, 1336, 1504, ..., .

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

a(n)==53 for n's: 22, 29, 203, 242, 374, 377, 493, 841, 899, 1073, 1247, 1298, 1342, 1363, 1562, 1711, ..., .

a(n)==59 for n's: 14, 28, 266, 434, 532, 868, 994, 1414, 1442, 1526, 1918, 2534, 2758, 2884, 2954, 3052, ..., .

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

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

a(n)==77 for n's: 41, 46, 92, 287, 533, 697, 782, 874, 1058, 1517, 1681, 1748, 1927, 2116, 2162, 2419, ..., .

a(n)==83 for n's: 26, 52, 494, 988, 1534, 1586, 2626, 2678, 2782, 3068, 3172, 3562, 3874, 4082, 4342, ..., .

a(n)==89 for n's: 58, 1682, 1798, 2726, 3422, 5974, 7946, 8642, 8758, 9106, 12934, 13166, 13282, 13978, ..., .

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..50000.
• Index entries for sequences related to Bernoulli numbers.

Crossrefs

Cf. A000367, A002445, A169980.

Programs

Mathematica

f[n_] := Block[{b = BernoulliB[2 n]}, Mod[Abs@ Numerator@ b, Denominator@ b]]; Array[f, 53, 0]

Formula

|A000367(n)| mod A002445(n).