cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A038610 Least common multiple of integers less than and prime to n.

This page as a plain text file.
%I A038610 #31 Jun 20 2019 02:58:18
%S A038610 1,1,2,3,12,5,60,105,280,63,2520,385,27720,6435,8008,45045,720720,
%T A038610 85085,12252240,2909907,3695120,1322685,232792560,37182145,1070845776,
%U A038610 128707425,2974571600,717084225,80313433200,215656441,2329089562800
%N A038610 Least common multiple of integers less than and prime to n.
%C A038610 If n is a prime power, tau(a(n)) is the number of times n occurs in A034699. (If n is not a prime power, it does not occur in A034699.) - _Franklin T. Adams-Watters_, Apr 01 2008
%C A038610 a(n) = lcm(A038566(n,k): k = 1..A000010(n)). - _Reinhard Zumkeller_, Sep 21 2013
%H A038610 T. D. Noe, <a href="/A038610/b038610.txt">Table of n, a(n) for n=1..200</a>
%F A038610 a(n) = e^[Sum_{k=1..n} (1-floor(n^k/k)+floor((n^k -1)/k))*Mangoldt(k)] where Mangoldt is the Mangoldt function. - _Anthony Browne_, Jun 16 2016
%e A038610 Since 1, 5, 7, and 11 are relatively prime to 12, a(12) = LCM(1,5,7,11) = 385.
%p A038610 A038610 := n -> ilcm(op(select(k->igcd(n,k)=1,[$1..n]))); # _Peter Luschny_, Jun 25 2011
%t A038610 Table[ LCM@@ Flatten[ Position[ GCD[ n, # ]& /@ Range[ n ], 1 ] ], {n, 32} ]
%t A038610 Join[{1},Table[LCM@@Select[Range[n-1],CoprimeQ[#,n]&],{n,2,40}]] (* _Harvey P. Dale_, Mar 05 2016 *)
%o A038610 (PARI) a(n) = local(r); r=1;for(i=1,n-1,if(gcd(i,n)==1,r=lcm(r,i)));r \\ _Franklin T. Adams-Watters_, Apr 01 2008
%o A038610 (Haskell)
%o A038610 a038610 = foldl lcm 1 . a038566_row
%o A038610 -- _Reinhard Zumkeller_, Sep 21 2013, Oct 04 2011
%Y A038610 Cf. A034699, A000005.
%K A038610 nonn,nice
%O A038610 1,3
%A A038610 _Wouter Meeussen_