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
KEYWORD
nonn
AUTHOR
Eric Chen, Nov 13 2014
STATUS
approved