The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A217863 a(n) = phi(lcm(1,2,3,...,n)), where phi is Euler's totient function. 4
1, 1, 2, 4, 16, 16, 96, 192, 576, 576, 5760, 5760, 69120, 69120, 69120, 138240, 2211840, 2211840, 39813120, 39813120, 39813120, 39813120, 875888640, 875888640, 4379443200, 4379443200, 13138329600, 13138329600, 367873228800, 367873228800, 11036196864000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
This is a composition f(g(x)). g(x) = lcm(1...x) and f(x) = phi(x), Euler's totient function. The sequence generated is the number of prime congruence classes (prime spokes) for wheel factorization in mod g(x).
First column of A096180. - Eric Desbiaux, Apr 23 2013
LINKS
FORMULA
a(n) = A000010(A003418(n)). - Omar E. Pol, Nov 25 2012
From Peter Bala, Feb 19 2019: (Start)
a(n) = Product_{k = 1..n} A072211(k).
With p denoting a prime, a(n) = ( Product_{p <= n} (p - 1) ) * ( Product_{p^2 <= n} p ) * ( Product_{p^3 <= n} p ) * ... . For example, a(16) = ((2-1)*(3-1)*(5-1)*(7-1)*(11-1)*(13-1)) * (2*3) * 2 * 2 = 138240. (End)
MAPLE
with(numtheory): a:=n->phi(lcm(seq(m, m=1..n))): seq(a(n), n=1..40); # Muniru A Asiru, Feb 20 2019
MATHEMATICA
EulerPhi[Table[LCM @@ Range[n], {n, 35}]] (* T. D. Noe, Oct 16 2012 *)
PROG
(Haskell)
a217863 = a000010 . a003418 -- Reinhard Zumkeller, Nov 24 2012
(PARI) a(n) = eulerphi(lcm(vector(n, k, k))); \\ Michel Marcus, Aug 25 2015
CROSSREFS
Cf. A000010 (Euler phi), A003418 (LCM), A072211, A173557.
Sequence in context: A370874 A337109 A210579 * A186108 A131560 A067709
KEYWORD
nonn,easy
AUTHOR
Joshua S.M. Weiner, Oct 13 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 08:06 EDT 2024. Contains 372850 sequences. (Running on oeis4.)