A219742 Bernoulli denominators with 8 divisors in increasing order (without repetitions).

30, 42, 66, 138, 282, 354, 498, 642, 1002, 1074, 1362, 1434, 1578, 2082, 2154, 2298, 2658, 2802, 2874, 3018, 3378, 3522, 3882, 3954, 4314, 4962, 5034, 5178, 5322, 5898, 6114, 7122, 7338, 7554, 7698, 7842, 7914, 8202, 8634, 8922, 8994, 9138, 9714, 10722

Offset

1,1

Comments

Let m, n >= 1 and let f(m) denote number of Bernoulli numbers less than or equal to 10^m having denominator divisible by a(n). For any n, f(m) = floor(10^m/(a(n)/6 - 1)). It appears that the fraction of even Bernoulli numbers with denominator 6 is not so close to 1/6.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Paul Erdős and Samuel S. Wagstaff, Jr., The fractional parts of the Bernoulli numbers, Illinois J. Math. 24 (1980), pp. 104-112.

Eric Weisstein's World of Mathematics, Bernoulli Number

Index entries for sequences related to Bernoulli numbers

Formula

a(n) = 6*A092307(n).

A002445 INTERSECT A138636.

Mathematica

6*Prime@Flatten@Position[Table[p = Prime[n]; Length@Select[Divisors[p - 1] + 1, PrimeQ], {n, 277}], 3]

Crossrefs

Cf. A002445, A092307, A114648, A138636.

Sequence in context: A226104 A091455 A367481 * A348557 A257832 A050776

Adjacent sequences: A219739 A219740 A219741 * A219743 A219744 A219745

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 29 2012

Status

approved