A217863 a(n) = phi(lcm(1,2,3,...,n)), where phi is Euler's totient function.

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

Offset: 1

Author

Joshua S.M. Weiner, Oct 13 2012

Keywords

• nonn
• easy

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

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010 (Euler phi), A003418 (LCM), A072211, A173557.

Programs

Haskell

a217863 = a000010 . a003418  -- Reinhard Zumkeller, Nov 24 2012

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 *)

PARI

a(n) = eulerphi(lcm(vector(n, k, k))); \\ Michel Marcus, Aug 25 2015

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)