|
%I #43 Feb 21 2019 08:21:39
%S 1,1,2,4,16,16,96,192,576,576,5760,5760,69120,69120,69120,138240,
%T 2211840,2211840,39813120,39813120,39813120,39813120,875888640,
%U 875888640,4379443200,4379443200,13138329600,13138329600,367873228800,367873228800,11036196864000
%N a(n) = phi(lcm(1,2,3,...,n)), where phi is Euler's totient function.
%C 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).
%C First column of A096180. - _Eric Desbiaux_, Apr 23 2013
%H Reinhard Zumkeller, <a href="/A217863/b217863.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000010(A003418(n)). - _Omar E. Pol_, Nov 25 2012
%F From _Peter Bala_, Feb 19 2019: (Start)
%F a(n) = Product_{k = 1..n} A072211(k).
%F 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)
%p with(numtheory): a:=n->phi(lcm(seq(m,m=1..n))): seq(a(n),n=1..40); # _Muniru A Asiru_, Feb 20 2019
%t EulerPhi[Table[LCM @@ Range[n], {n, 35}]] (* _T. D. Noe_, Oct 16 2012 *)
%o (Haskell)
%o a217863 = a000010 . a003418 -- _Reinhard Zumkeller_, Nov 24 2012
%o (PARI) a(n) = eulerphi(lcm(vector(n, k, k))); \\ _Michel Marcus_, Aug 25 2015
%Y Cf. A000010 (Euler phi), A003418 (LCM), A072211, A173557.
%K nonn,easy
%O 1,3
%A _Joshua S.M. Weiner_, Oct 13 2012
|
