A083554 -id:A083554 - cp's OEIS frontend

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

Labos Elemer, May 22 2003

nonn

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

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

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

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

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 *)

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

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

A083549 Quotient if least common multiple (lcm) of cototient values of consecutive integers is divided by the greatest common divisor (gcd) of the same pair of consecutive numbers.

Original entry on oeis.org

0, 1, 2, 2, 4, 4, 4, 12, 2, 6, 8, 8, 8, 56, 56, 8, 12, 12, 12, 12, 12, 12, 16, 80, 70, 126, 144, 16, 22, 22, 16, 208, 234, 198, 264, 24, 20, 12, 40, 24, 30, 30, 24, 56, 56, 24, 32, 224, 210, 570, 532, 28, 36, 60, 480, 672, 70, 30, 44, 44, 32, 864, 864, 544, 782, 46, 36, 900

Offset: 1

Labos Elemer, May 22 2003

nonn

			n=33: cototient(33) = 33-20 = 13, cototient(34) = 34-16 = 18;
lcm(13,18) = 234, gcd(13,18) = 1, so a(34) = 234.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A051953, A083538, A083539, A083540, A083541, A083542, A083543, A083544, A083545, A083546, A083547, A083548, A083549, A083550, A083551, A083552, A083553, A083554, A083555, A049586.

f[x_] := x-EulerPhi[x]; Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 69}]
(* Second program: *)
Map[Apply[LCM, #]/Apply[GCD, #] &@ Map[# - EulerPhi@ # &, #] &, Partition[Range[69], 2, 1]] (* Michael De Vlieger, Mar 17 2018 *)

a(n) = lcm(A051953(n), A051952(n+1))/gcd(A051953(n), A051952(n+1)) = lcm(cototient(n+1), cototient(n))/A049586(n).

cp's OEIS Frontend

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

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