OFFSET
1,1
COMMENTS
Divisibility through terms of A008578 is a consequence of the Staudt-Clausen theorem.
The first 250 entries are all different. Is this true in general?
Would sorting the entries yield the full A090801?
a(n) > 1 is the largest number k such that x*y^p == y*x^p (mod k) for all integers x and y, where p = prime(n). Example: x*y^19 == y*x^19 (mod 798). - Michel Lagneau, Apr 19 2012
Comment from Herbert Kociemba, May 29 2020: (Start)
For each n there is exactly one member of the sequence whose factorization has prime(n) as its largest prime factor, namely a(n). From this we conclude:
1. All elements of the sequence are different.
2. Not all denominators of Bernoulli numbers appear in this sequence. For example the denominator of B(20), 330=2*3*5*11 never appears because the unique sequence element with largest prime divisor 11=prime(5) is a(5)=2*3*11. (End)
LINKS
Peter Luschny, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, von Staudt-Clausen Theorem.
MAPLE
seq(denom(bernoulli(ithprime(n)-1)), n=1..38); # Peter Luschny, Jul 14 2019
MATHEMATICA
Table[Denominator[BernoulliB[n - 1]], {n, Prime[Range[38]]}] (* Harvey P. Dale, Apr 22 2012 *)
Table[GCD @@ Table[(n^k - n), {n, 2, 13}], {k, Prime[Range[100]]}] (* Increase n to 80 and k to 1000 for first thousand terms. - Herbert Kociemba, May 05 2020 *)
a[i_] := Times @@ Select[Prime[Range[i]], Mod[Prime[i] - 1, # - 1] == 0&]; Table[a[i], {i, 1, 100}](* Herbert Kociemba, May 06 2020 *)
PROG
(PARI) a(n)=denominator(bernfrac(prime(n)-1)) \\ Charles R Greathouse IV, Apr 30 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Oct 05 2009
EXTENSIONS
Edited by Peter Luschny, Jul 14 2019
STATUS
approved