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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.

%I A211384 #29 Oct 05 2020 12:34:02
%S A211384 1,3,4,6,7,12,13,18,20,21,22,24,25,39,56,72,73,120,121,126,156,198,
%T A211384 199,216,217,225,240,312,313,336,337,360,396,438,455,480,481,726,800,
%U A211384 882,883,936,937,990,1120,1194,1195,1296,1300,1302,1460,1800,1801,1920
%N 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.
%C A211384 Conjecture: 10 and 25 are the only composite numbers n for which a(n) = a(n-1) + 1. - _J. Lowell_, Oct 03 2020
%H A211384 Alois P. Heinz, <a href="/A211384/b211384.txt">Table of n, a(n) for n = 1..10000</a>
%e A211384 a(6) = 12 is divisible by a(1) = 1, a(2) = 3, a(3) = 4.
%p A211384 a:= proc(n) a(n):= `if`(n<3, 2*n-1, (h-> ceil((a(n-1)+1)/h)*h)
%p A211384     (ilcm(map(a, numtheory[divisors](n) minus {1, n})[]))) end:
%p A211384 seq(a(n), n=1..100);  # _Alois P. Heinz_, Feb 07 2013
%t A211384 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_ *)
%Y A211384 Cf. A222208, A222209.
%K A211384 nonn
%O A211384 1,2
%A A211384 _J. Lowell_, Feb 07 2013
%E A211384 More terms from _Alois P. Heinz_, Feb 07 2013