%I #23 Mar 15 2018 04:13:04
%S 2,2,6,15,30,12,72,99,154,210,30,90,420,483,598,754,870,110,1155,1260,
%T 156,1599,1804,132,600,2550,2703,2862,756,72,4095,4420,4692,5106,5550,
%U 650,702,6723,7138,7654,8010,342,9120,2352,9702,1155,1295,12543,12882
%N Quotient of LCM of prime(n+1)-1 and prime(n)-1 and GCD of the same two numbers.
%H Robert Israel, <a href="/A083555/b083555.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = lcm(A006093(n+1), A006093(n))/gcd(A006093(n+1), A006093(n));
%F a(n) = A083554(n)/A058263(n).
%F a(n) = A051537(A006093(n+1), A006093(n)). - _Robert Israel_, Jun 11 2017
%e n=25: prime(25)=97, prime(26)=101; a(25) = lcm(96,100)/gcd(96,100) = 2400/4 = 600.
%p P:= seq(ithprime(i),i=1..100):
%p 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
%t f[x_] := Prime[x]-1 Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 1, 128}]
%t (* Second program: *)
%t Table[Apply[LCM[#1, #2]/GCD[#1, #2] &, Prime[n + {1, 0}] - 1], {n, 49}] (* _Michael De Vlieger_, Jun 11 2017 *)
%o (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
%Y Cf. A006093, A083538..A083554, A051537, A058263.
%K nonn
%O 1,1
%A _Labos Elemer_, May 22 2003