A099795 Least common multiple of 1, 2, 3, ..., prime(n)-1.

1, 2, 12, 60, 2520, 27720, 720720, 12252240, 232792560, 80313433200, 2329089562800, 144403552893600, 5342931457063200, 219060189739591200, 9419588158802421600, 3099044504245996706400, 164249358725037825439200, 9690712164777231700912800

Offset: 1

Author

Ray Chandler, Oct 29 2004

Keywords

• nonn

Comments

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

Examples

			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
		

Links

• Robert Israel, Table of n, a(n) for n = 1..342

Crossrefs

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

Cf. A002110, A007947, A053589.

Programs

Magma

[Lcm([2..p-1]): p in PrimesUpTo(70)]; // Bruno Berselli, Feb 06 2015

Maple

Primes:= select(isprime, [2,$3..100]):
seq(ilcm($2..Primes[i]-1),i=1..nops(Primes)); # Robert Israel, Jul 19 2016

Mathematica

LCM@@Range[#]&/@(Prime[Range[20]]-1) (* Harvey P. Dale, Jan 30 2015 *)

Formula

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

a(n) = A038610(A000040(n)). - Anthony Browne, Jul 19 2016

Rad(a(n)) = A007947(a(n)) = A002110(n-1). - David James Sycamore, Oct 24 2024

Extensions

a(18) from Bruno Berselli, Feb 06 2015