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

Author

Arkadiusz Wesolowski, Nov 29 2012

Keywords

• nonn

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

Crossrefs

Cf. A002445, A092307, A114648, A138636.

Programs

Mathematica

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

Formula

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

A002445 INTERSECT A138636.