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First multiple of n in A025487.
2

%I #11 Dec 30 2020 08:23:13

%S 1,2,6,4,30,6,210,8,36,30,2310,12,30030,210,30,16,510510,36,9699690,

%T 60,210,2310,223092870,24,900,30030,216,420,6469693230,30,

%U 200560490130,32,2310,510510,210,36,7420738134810,9699690,30030,120,304250263527210

%N First multiple of n in A025487.

%H Amiram Eldar, <a href="/A073039/b073039.txt">Table of n, a(n) for n = 1..2370</a>

%F 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

%t 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 *)

%Y Cf. A002110, A025487.

%K nonn

%O 1,2

%A _Jeff Burch_, Aug 22 2002