A058250 GCD of n-th primorial number and its totient.

1, 1, 2, 2, 6, 30, 30, 30, 30, 330, 2310, 2310, 2310, 2310, 2310, 53130, 690690, 20030010, 20030010, 20030010, 20030010, 20030010, 20030010, 821230410, 821230410, 821230410, 821230410, 13960916970, 739928599410, 739928599410

Offset: 0

Author

Labos Elemer, Dec 05 2000

Keywords

• nonn
• look

Examples

			a(6) = gcd(30030,5760) = 30.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002110, A000010, A005867, A038110.

Programs

Maple

[seq(igcd(product(ithprime(k), k=1..m), product(ithprime(k)-1, k=1..m)), m=1..50)];

Mathematica

GCD[#,EulerPhi[#]]&/@Rest[FoldList[Times,1,Prime[Range[30]]]] (* Harvey P. Dale, Dec 19 2012 *)
Fold[Append[#1, {#1, #2, GCD[#1, #2]} & @@ {#4 #1, #2 (#4 - 1)} & @@ Append[#1[[-1]], #2]] &, {{1, 1, 1}}, Prime@ Range[29]][[All, -1]] (* Michael De Vlieger, Apr 25 2019 *)

PARI

a(n) = my(pr=prod(k=1, n, prime(k))); gcd(pr, eulerphi(pr)); \\ Michel Marcus, Apr 13 2019

Formula

a(n) = gcd(A002110(n), A000010(A002110(n))) = gcd(A002110(n), A005867(n)).

a(n) = A005867(n) / A038110(n+1). For example: For n = 4: a(4) = 48 / 8 = 6. - Jamie Morken, Apr 12 2019

Extensions

a(0) = 1 inserted by Michael De Vlieger, Apr 13 2019