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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

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

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: A196202 A135569 A210579 * A186108 A131560 A067709

Adjacent sequences:  A217860 A217861 A217862 * A217864 A217865 A217866

KEYWORD

nonn,easy

AUTHOR

Joshua S.M. Weiner, Oct 13 2012

STATUS

approved

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)