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a(n) = smallest integer that is > n and is a multiple of every proper divisor of n.
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%I #11 Sep 16 2015 13:45:19

%S 3,4,6,6,12,8,12,12,20,12,24,14,28,30,24,18,36,20,40,42,44,24,48,30,

%T 52,36,56,30,60,32,48,66,68,70,72,38,76,78,80,42,84,44,88,90,92,48,96,

%U 56,100,102,104,54,108,110,112,114,116,60

%N a(n) = smallest integer that is > n and is a multiple of every proper divisor of n.

%C a(n) = A048671(n) + n.

%e The proper divisors of 16 are 1,2,4,8. a(16)=24 is the smallest integer which is both > 16 and is a multiple of 1, of 2, of 4 and of 8.

%t a = {}; For[n = 2, n < 60, n++, i = n + 1; While[Length[Union[Mod[i, Complement[Divisors[n], {n}]]]] > 1, i++ ]; AppendTo[a, i]]; a (* _Stefan Steinerberger_, Aug 30 2008 *)

%Y Cf. A048671.

%K nonn

%O 2,1

%A _Leroy Quet_, Dec 31 2007

%E More terms from _Stefan Steinerberger_, Aug 30 2008