A099795 - OEIS

%I #21 Oct 25 2024 09:35:24

%S 1,2,12,60,2520,27720,720720,12252240,232792560,80313433200,

%T 2329089562800,144403552893600,5342931457063200,219060189739591200,

%U 9419588158802421600,3099044504245996706400,164249358725037825439200,9690712164777231700912800

%N Least common multiple of 1, 2, 3, ..., prime(n)-1.

%C Alternative definition: a(n) = Product{i = 1..(n-1)}prime(i)^e_i, where prime(i)^e_i is the greatest power of prime(i) which does not exceed prime(n). Every term is a product of prime powers, and also of primorial powers(the greatest of which is A002110(n-1); see Example and A053589). - _David James Sycamore_, Oct 24 2024

%H Robert Israel, <a href="/A099795/b099795.txt">Table of n, a(n) for n = 1..342</a>

%F a(n) = (A094998(n)-1) / A099796(n).

%F a(n) = A038610(A000040(n)). - _Anthony Browne_, Jul 19 2016

%F Rad(a(n)) = A007947(a(n)) = A002110(n-1). - _David James Sycamore_, Oct 24 2024

%e For n = 7, prime(7) = 17, using the alternative definition (see Comment), a(7) = 2^4*3^2*5^1*7^1*11^1*13^1 = 16*9*5*7*11*13 = 720720 = 24*30030 = 2^2*6*30030 = A002110(1)^2*A002110(2)*A002110(6). - _David James Sycamore_, Oct 24 2024

%p Primes:= select(isprime, [2,$3..100]):

%p seq(ilcm($2..Primes[i]-1),i=1..nops(Primes)); # _Robert Israel_, Jul 19 2016

%t LCM@@Range[#]&/@(Prime[Range[20]]-1) (* _Harvey P. Dale_, Jan 30 2015 *)

%o (Magma) [Lcm([2..p-1]): p in PrimesUpTo(70)]; // _Bruno Berselli_, Feb 06 2015

%Y Cf. A094998, A099794, A099796, A038610, A000040.

%Y Cf. A002110, A007947, A053589.

%K nonn

%O 1,2

%A _Ray Chandler_, Oct 29 2004

%E a(18) from _Bruno Berselli_, Feb 06 2015