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LCM of n-th primorial number and its Euler totient.
1

%I #22 Aug 16 2024 21:12:39

%S 1,2,6,120,1680,36960,5765760,1568286720,536354058240,24672286679040,

%T 2861985254768640,2661646286934835200,3545312854197200486400,

%U 5814313080883408797696000,10500649424075436288638976000

%N LCM of n-th primorial number and its Euler totient.

%F a(n) = LCM(A002110(n), A000010(A002110(n))) = LCM(A002110(n), A005867(n)).

%F a(n) = A009262(A002110(n)). - _Michel Marcus_, Apr 27 2022

%e a(6) = LCM(30030,5760) = 5765760.

%p [seq(ilcm(product(ithprime(k), k=1..m), product(ithprime(k)-1, k=1..m)), m=1..20)];

%t LCM[#,EulerPhi[#]]&/@Rest[FoldList[Times,1,Prime[Range[15]]]] (* _Harvey P. Dale_, Nov 29 2011 *)

%o (PARI) P(n) = prod(k=1, n, prime(k)); \\ A002110

%o a(n) = my(p= P(n)); lcm(p, eulerphi(p)); \\ _Michel Marcus_, Apr 27 2022

%Y Cf. A002110, A000010, A005867, A009262.

%K nonn

%O 0,2

%A _Labos Elemer_, Dec 05 2000

%E a(0)=1 inserted by _Jamie Morken_, Apr 27 2022