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

0,6

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A000367, A002445, A169980.

Sequence in context: A133750 A203925 A198597 * A332300 A242193 A326727

Adjacent sequences: A180312 A180313 A180314 * A180316 A180317 A180318

Keyword

nonn

Author

Robert G. Wilson v, Aug 27 2010

Status

approved