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

1,3

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

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A034699, A000005.

Sequence in context: A282216 A245678 A124444 * A334313 A325760 A056819

Adjacent sequences: A038607 A038608 A038609 * A038611 A038612 A038613

Keyword

nonn,nice

Author

Wouter Meeussen

Status

approved