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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

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OFFSET

0,3

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

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)

FORMULA

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

EXAMPLE

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

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 *)

PROG