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A246006 a(2n) = numerator of |Bernoulli(2n)|, a(2n+1) = Euler(2n). 4
1, 1, 1, 1, 1, 5, 1, 61, 1, 1385, 5, 50521, 691, 2702765, 7, 199360981, 3617, 19391512145, 43867, 2404879675441, 174611, 370371188237525, 854513, 69348874393137901, 236364091, 15514534163557086905, 8553103, 4087072509293123892361, 23749461029, 1252259641403629865468285 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Primes p which divide at least one a(n) for n<=p-2 are called weakly-irregular primes. For example, 19|a(11), 31|a(23), 37|a(32), 43|a(13), 47|a(15), 59|a(44), 61|a(7), ... - Eric Chen, Nov 26 2014

The weakly-irregular primes below 500 are 19, 31, 37, 43, 47, 59, 61, 67, 71, 79, 101, 103, 131, 137, 139, 149, 157, 193, 223, 233, 241, 251, 257, 263, 271, 277, 283, 293, 307, 311, 347, 349, 353, 359, 373, 379, 389, 401, 409, 419, 421, 433, 461, 463, 467, 491. - Eric Chen, Nov 26 2014

A prime can divide more than one a(n) for n<=p-2; for example, 67 divides both a(27) and a(58); additional examples are 101, 149, 157, 241, 263, 307, 311, ... . - Eric Chen, Nov 26 2014

Smallest values of k such that the n-th weakly-irregular prime divides a(k) are 11, 23, 32, 13, 15, 44, 7, 27, 29, 19, 63, 24, 22, 43, 129, 130, 62, 75, ... . - Eric Chen, Nov 26 2014

Smallest prime factors (>= n+2) of a(n) are 1, 1, 1, 1, 1, 1, 1, 61, 1, 277, 1, 19, 691, 43, 1, 47, 3617, 228135437, 43867, 79, 283, 41737, 131, 31, 103, 2137, 657931, 67, 9349, 71, ... . - Eric Chen, Nov 26 2014

The irregular pairs are (61, 7), (277, 9), (19, 11), (2659, 11), (691, 12), (43, 13), (967, 13), (47, 15), (4241723, 15), (3617, 16), (228135437, 17), (43867, 18), (79, 19), (349, 19), (84224971, 19), ... . - Eric Chen, Nov 26 2014

LINKS

Eric Chen, Table of n, a(n) for n = 0..199

Peter Luschny, Irregular primes

Wikipedia, Irregular prime

EXAMPLE

Euler(10) = 50521, so a(11) = 50521.

Bernoulli(12) = 691/2730, so a(12) = 691.

MATHEMATICA

a246006[n_] := If[EvenQ[n], Abs[Numerator[BernoulliB[n]]], Abs[EulerE[n-1]]]; Table[a246006[n], {n, 0, 99}]

CROSSREFS

Cf. A027641, A122045, A000367, A028296, A000111, A000364, A000182.

Cf. A050970, A050971, A068205.

Sequence in context: A144342 A144268 A013988 * A050970 A335955 A138548

Adjacent sequences:  A246003 A246004 A246005 * A246007 A246008 A246009

KEYWORD

nonn

AUTHOR

Eric Chen, Nov 13 2014

STATUS

approved

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)