A169980 Numerator(Bernoulli(2n)) mod denominator(Bernoulli(2n)).

0, 1, 29, 1, 29, 5, 2039, 1, 463, 775, 289, 17, 2039, 1, 811, 12899, 463, 1, 1280537, 1, 11519, 1, 637, 41, 31933, 5, 1507, 775, 811, 53, 34488049, 1, 463, 62483, 29, 289, 91560011, 1, 29, 37, 182293, 77, 2346073, 1, 56003, 230759, 1333, 1, 3051091, 1, 28859, 61, 1507

Offset

0,3

Comments

From Robert G. Wilson v, Aug 27 2010: (Start)

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

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

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, ..., .

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

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

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

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: 29, 203, 377, 493, 841, 899, 1073, 1247, 1363, 1711, 1943, 2059, 2117, 2813, 2929, 2987, ..., .

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, 287, 533, 697, 1517, 1681, 1927, 2419, 2747, 2911, 3239, 3731, 3977, 4141, 4387, ..., .

(End)

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..50000.

Index entries for sequences related to Bernoulli numbers. [From Robert G. Wilson v, Aug 27 2010]

Formula

A000367(n) mod A002445(n). [Robert G. Wilson v, Aug 27 2010]

Mathematica

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

Prog

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

Crossrefs

Cf. A000367, A002445, A180315. [Robert G. Wilson v, Aug 27 2010]

Sequence in context: A040866 A040867 A040868 * A040869 A111881 A040833

Adjacent sequences: A169977 A169978 A169979 * A169981 A169982 A169983

Keyword

nonn

Author

Robert G. Wilson v, Aug 19 2010

Status

approved