A073039 First multiple of n in A025487.

1, 2, 6, 4, 30, 6, 210, 8, 36, 30, 2310, 12, 30030, 210, 30, 16, 510510, 36, 9699690, 60, 210, 2310, 223092870, 24, 900, 30030, 216, 420, 6469693230, 30, 200560490130, 32, 2310, 510510, 210, 36, 7420738134810, 9699690, 30030, 120, 304250263527210

Offset: 1

Author

Jeff Burch, Aug 22 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2370

Crossrefs

Cf. A002110, A025487.

Programs

Mathematica

prim[p_] := Product[Prime[i], {i, PrimePi[p]}]; a[n_] := Module[{f = FactorInteger[n]}, p = f[[;; , 1]]; e = f[[;; , 2]]; LCM @@ ((prim /@ p)^e)]; Array[a, 50] (* Amiram Eldar, Dec 30 2020 *)

Formula

If n = 2^e_1 * 3^e_2 * ... * prime(k)^e_k, then a(n) = 2^max(e_1, e_2, ..., e_k) * 3^max(e_2, ..., e_k) * ... * prime(k-1)^max(e_{k-1}, e_k) * prime(k)^e_k = lcm_{i=1}^k prime(k)#^e_k. In particular, if p prime, a(p) = p# (primorial, A002110). When gcd(n,m) = 1, a(n*m) = lcm(a(n), a(m)). Also, a(n^k) = a(n)^k. - Franklin T. Adams-Watters, Oct 24 2006