A088303 - OEIS

%I #14 Mar 28 2015 20:21:48

%S 1,2,3,4,10,6,420,56,63,120,1155,792,180180,121080960,5405400,5765760,

%T 14294280,10585935360,969969,221707200,219988969200,853572720,

%U 206137811880,25700298624,368103235500,306261891936000,9302704967556000

%N Smallest integer value of n!/(m_1!*m_2!*...*m_k!), where 1=m_1 < m_2 < ... is the sequence of integers coprime to n.

%H Charles R Greathouse IV, <a href="/A088303/b088303.txt">Table of n, a(n) for n = 1..748</a>

%e a(9) = 9!/{1!*2!*4!*5!} = 63 which is not divisible by 7!.

%p A := proc (n) local x, i; x := n!; for i to n while x = floor(x) do if gcd(i,n) = 1 and `mod`(x,i!) = 0 then x := x/i! fi od; RETURN(x) end # Michael Lugo

%o (PARI) a(n)=my(N=n!); for(k=2,n,if(gcd(n,k)>1,next); if(N%k!, return(N), N/=k!)); N \\ _Charles R Greathouse IV_, Oct 20 2013

%Y Cf. A088302, A074199.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Sep 30 2003

%E Corrected and extended by _Ray Chandler_, Oct 06 2003

%E Edited by _Max Alekseyev_, Mar 28 2015