A211384 a(1) = 1, a(2) = 3; for n>2, a(n) = smallest number > a(n-1) such that a(n) is divisible by a(d) for all divisors d of n.

1, 3, 4, 6, 7, 12, 13, 18, 20, 21, 22, 24, 25, 39, 56, 72, 73, 120, 121, 126, 156, 198, 199, 216, 217, 225, 240, 312, 313, 336, 337, 360, 396, 438, 455, 480, 481, 726, 800, 882, 883, 936, 937, 990, 1120, 1194, 1195, 1296, 1300, 1302, 1460, 1800, 1801, 1920

Offset: 1

Author

J. Lowell, Feb 07 2013

Keywords

• nonn

Comments

Conjecture: 10 and 25 are the only composite numbers n for which a(n) = a(n-1) + 1. - J. Lowell, Oct 03 2020

Examples

			a(6) = 12 is divisible by a(1) = 1, a(2) = 3, a(3) = 4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A222208, A222209.

Programs

Maple

a:= proc(n) a(n):= `if`(n<3, 2*n-1, (h-> ceil((a(n-1)+1)/h)*h)
    (ilcm(map(a, numtheory[divisors](n) minus {1, n})[]))) end:
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 07 2013

Mathematica

a[1] = 1; a[2] = 3; a[n_] := a[n] = (Ceiling[(a[n-1]+1)/#]*#&)[LCM @@ Map[a, Most[Divisors[n]]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Mar 27 2017, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Feb 07 2013