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

1, 1, 2, 3, 12, 5, 60, 105, 280, 63, 2520, 385, 27720, 6435, 8008, 45045, 720720, 85085, 12252240, 2909907, 3695120, 1322685, 232792560, 37182145, 1070845776, 128707425, 2974571600, 717084225, 80313433200, 215656441, 2329089562800

Offset: 1

Author

Wouter Meeussen

Keywords

• nonn
• nice

Comments

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

a(n) = lcm(A038566(n,k): k = 1..A000010(n)). - Reinhard Zumkeller, Sep 21 2013

Examples

			Since 1, 5, 7, and 11 are relatively prime to 12, a(12) = LCM(1,5,7,11) = 385.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..200

Crossrefs

Cf. A034699, A000005.

Programs

Haskell

a038610 = foldl lcm 1 . a038566_row
-- Reinhard Zumkeller, Sep 21 2013, Oct 04 2011

Maple

A038610 := n -> ilcm(op(select(k->igcd(n,k)=1,[$1..n]))); # Peter Luschny, Jun 25 2011

Mathematica

Table[ LCM@@ Flatten[ Position[ GCD[ n, # ]& /@ Range[ n ], 1 ] ], {n, 32} ]
Join[{1},Table[LCM@@Select[Range[n-1],CoprimeQ[#,n]&],{n,2,40}]] (* Harvey P. Dale, Mar 05 2016 *)

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

Formula

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