A119250 Smallest number greater than n having a maximal number of divisors d such that d-1 are divisors of n.

2, 6, 4, 6, 6, 12, 8, 30, 20, 66, 12, 60, 14, 24, 48, 30, 18, 84, 20, 30, 88, 276, 24, 60, 78, 42, 140, 30, 30, 84, 32, 90, 204, 630, 72, 60, 38, 60, 280, 90, 42, 84, 44, 60, 60, 1128, 48, 60, 200, 66, 468, 210, 54, 84, 168, 120, 580, 1770, 60, 420, 62, 96, 440, 90, 462, 84

Offset: 1

Author

Reinhard Zumkeller, May 10 2006

Keywords

• nonn

Comments

Let x(0)=1 and x(k) = lcm(x(k-1), d(k)) with 1 <= k <= A000005(n), where d(k) = (k-th divisor of n): A057643(n)=x(A000005(n)) and a(n) = Min{x(i): x(i)>n}.

a(n) = n+1 iff n is an odd prime;

A057643(n) = x(A000005(n)) and a(n) = Min{x(i): x(i)>n}.

Crossrefs

Cf. A027750.