A058254 a(n) = lcm{prime(i)-1, i=1..n}.

1, 1, 2, 4, 12, 60, 60, 240, 720, 7920, 55440, 55440, 55440, 55440, 55440, 1275120, 16576560, 480720240, 480720240, 480720240, 480720240, 480720240, 480720240, 19709529840, 19709529840, 39419059680, 197095298400, 3350620072800, 177582863858400, 532748591575200

Offset: 0

Author

Labos Elemer, Dec 06 2000

Keywords

• nonn

Comments

A002110(n) divides b^(a(n)+1) - b for every integer b. - Thomas Ordowski, Nov 24 2014

What is the asymptotic growth of this sequence? a(n) <= A005867(n) <= A002110(n) < e^((1 + o(1))n log n) but this is a large overestimate. - Charles R Greathouse IV, Dec 03 2014

Alexander Kalmynin gives a proof that log a(n) = O(p log log p/log p) where p is the n-th prime, see the MathOverflow link. - Charles R Greathouse IV, Sep 17 2021

Examples

			For n = 5 and 6: a(5) = a(6) = LCM[1, 2, 4, 6, 10, 12] = 60.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• MathOverflow, Asymptotics of lcm((2-1), (3-1), (5-1), (7-1), (11-1), ..., pn-1)

Crossrefs

Cf. A000010, A000142, A002110, A003418, A005867, A006093, A055769, A058255.

Programs

Haskell

a058254 n = a058254_list !! (n-1)
a058254_list = scanl1 lcm a006093_list
-- Reinhard Zumkeller, May 01 2013

Maple

seq(ilcm(seq(ithprime(i)-1,i=1..n)), n=0..100); # Robert Israel, Nov 24 2014

Mathematica

Table[LCM @@ (Prime@ Range[1, n] - 1), {n, 27}] (* Michael De Vlieger, Dec 31 2016 *)

PARI

a(n)=lcm(apply(p->p-1, primes(n))) \\ Charles R Greathouse IV, Dec 03 2014

Formula

a(n) = A002322(A002110(n)). - Thomas Ordowski, Nov 24 2014

Extensions

Offset corrected by Reinhard Zumkeller, May 01 2013

a(0)=1 prepended by Alois P. Heinz, Apr 01 2021