%I #9 Jan 28 2019 23:50:10
%S 0,1,1,1,1,5,691,1,47,775,41,17,691,1,59,12899,47,1,638653,1,2011,1,
%T 53,41,14477,5,83,775,59,53,22298681,1,47,62483,1,289,48540859,1,1,37,
%U 47717,77,1058237,1,5407,230759,77,1,1450679,1,4471,61,83,101,71532367
%N AbsoluteValue(Numerator(Bernoulli(2n))) mod denominator(Bernoulli(2n)).
%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, 37, 41, 47, 49, 53, 59, 61, 65, 77, 83, 89, 101, 113, 137, 161, 167, 169, 173, ..., .
%C 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, ..., .
%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)==37 for n's: 39, 507, 1209, 1677, 3783, 4251, 5421, 5811, 6123, 6357, 6513, 7527, 7683, 7761, 8229, ..., .
%C a(n)==41 for n's: 10, 23, 123, 161, 170, 391, 437, 529, 610, 710, 851, 1010, 1081, 1127, 1357, 1403, ..., .
%C a(n)==47 for n's: 8, 16, 32, 64, 152, 248, 304, 376, 472, 496, 752, 824, 872, 992, 1256, 1336, 1504, ..., .
%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: 22, 29, 203, 242, 374, 377, 493, 841, 899, 1073, 1247, 1298, 1342, 1363, 1562, 1711, ..., .
%C a(n)==59 for n's: 14, 28, 266, 434, 532, 868, 994, 1414, 1442, 1526, 1918, 2534, 2758, 2884, 2954, 3052, ..., .
%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, 46, 92, 287, 533, 697, 782, 874, 1058, 1517, 1681, 1748, 1927, 2116, 2162, 2419, ..., .
%C a(n)==83 for n's: 26, 52, 494, 988, 1534, 1586, 2626, 2678, 2782, 3068, 3172, 3562, 3874, 4082, 4342, ..., .
%C a(n)==89 for n's: 58, 1682, 1798, 2726, 3422, 5974, 7946, 8642, 8758, 9106, 12934, 13166, 13282, 13978, ..., .
%H Robert G. Wilson v, <a href="/A180315/b180315.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>
%F |A000367(n)| mod A002445(n).
%t f[n_] := Block[{b = BernoulliB[2 n]}, Mod[Abs@ Numerator@ b, Denominator@ b]]; Array[f, 53, 0]
%Y Cf. A000367, A002445, A169980.
%K nonn
%O 0,6
%A _Robert G. Wilson v_, Aug 27 2010