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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}] PROG (Python) from sympy import euler, bernoulli def A246006(n): return abs(euler(n-1)) if n&1 else abs(bernoulli(n)).p # Chai Wah Wu, Apr 15 2023 CROSSREFS Cf. A027641, A122045, A000367, A028296, A000111, A000364, A000182. Cf. A050970, A050971, A068205. Sequence in context: A013988 A340472 A342318 * 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 February 21 10:54 EST 2024. Contains 370233 sequences. (Running on oeis4.)