A083555 Quotient of LCM of prime(n+1)-1 and prime(n)-1 and GCD of the same two numbers.

2, 2, 6, 15, 30, 12, 72, 99, 154, 210, 30, 90, 420, 483, 598, 754, 870, 110, 1155, 1260, 156, 1599, 1804, 132, 600, 2550, 2703, 2862, 756, 72, 4095, 4420, 4692, 5106, 5550, 650, 702, 6723, 7138, 7654, 8010, 342, 9120, 2352, 9702, 1155, 1295, 12543, 12882

Offset: 1

Author

Labos Elemer, May 22 2003

Keywords

• nonn

Examples

			n=25: prime(25)=97, prime(26)=101; a(25) = lcm(96,100)/gcd(96,100) = 2400/4 = 600.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006093, A083538..A083554, A051537, A058263.

Programs

Maple

P:= seq(ithprime(i),i=1..100):
seq(ilcm(P[i+1]-1,P[i]-1)/igcd(P[i+1]-1,P[i]-1),i=1..99); # Robert Israel, Jun 11 2017

Mathematica

f[x_] := Prime[x]-1 Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 1, 128}]
(* Second program: *)
Table[Apply[LCM[#1, #2]/GCD[#1, #2] &, Prime[n + {1, 0}] - 1], {n, 49}] (* Michael De Vlieger, Jun 11 2017 *)

PARI

first(n)=my(v=vector(n),p=2,k,g); forprime(q=3,, g=gcd(p-1,q-1); v[k++]=(p-1)*(q-1)/g^2; p=q; if(k==n, break)); v \\ Charles R Greathouse IV, Jun 11 2017

Formula

a(n) = lcm(A006093(n+1), A006093(n))/gcd(A006093(n+1), A006093(n));

a(n) = A083554(n)/A058263(n).

a(n) = A051537(A006093(n+1), A006093(n)). - Robert Israel, Jun 11 2017