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A058254 a(n) = lcm{prime(i)-1, i=1..n}. 12

%I #46 Sep 18 2021 00:27:17

%S 1,1,2,4,12,60,60,240,720,7920,55440,55440,55440,55440,55440,1275120,

%T 16576560,480720240,480720240,480720240,480720240,480720240,480720240,

%U 19709529840,19709529840,39419059680,197095298400,3350620072800,177582863858400,532748591575200

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

%C A002110(n) divides b^(a(n)+1) - b for every integer b. - _Thomas Ordowski_, Nov 24 2014

%C 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

%C 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

%H Reinhard Zumkeller, <a href="/A058254/b058254.txt">Table of n, a(n) for n = 0..1000</a>

%H MathOverflow, <a href="https://mathoverflow.net/questions/404131/asymptotics-of-operatornamelcm-2-1-3-1-5-1-7-1-11-1-dotsc">Asymptotics of lcm((2-1), (3-1), (5-1), (7-1), (11-1), ..., pn-1)</a>

%F a(n) = A002322(A002110(n)). - _Thomas Ordowski_, Nov 24 2014

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

%p seq(ilcm(seq(ithprime(i)-1,i=1..n)), n=0..100); # _Robert Israel_, Nov 24 2014

%t Table[LCM @@ (Prime@ Range[1, n] - 1), {n, 27}] (* _Michael De Vlieger_, Dec 31 2016 *)

%o (Haskell)

%o a058254 n = a058254_list !! (n-1)

%o a058254_list = scanl1 lcm a006093_list

%o -- _Reinhard Zumkeller_, May 01 2013

%o (PARI) a(n)=lcm(apply(p->p-1, primes(n))) \\ _Charles R Greathouse IV_, Dec 03 2014

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

%K nonn

%O 0,3

%A _Labos Elemer_, Dec 06 2000

%E Offset corrected by _Reinhard Zumkeller_, May 01 2013

%E a(0)=1 prepended by _Alois P. Heinz_, Apr 01 2021

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)