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A208570 LCM of n and smallest nondivisor of n.

%I A208570 #28 Mar 13 2018 04:16:12
%S A208570 2,6,6,12,10,12,14,24,18,30,22,60,26,42,30,48,34,36,38,60,42,66,46,
%T A208570 120,50,78,54,84,58,60,62,96,66,102,70,180,74,114,78,120,82,84,86,132,
%U A208570 90,138,94,240,98,150,102,156,106,108,110,168,114,174,118,420,122
%N A208570 LCM of n and smallest nondivisor of n.
%C A208570 a(n) = 2*n for all odd numbers.
%H A208570 Alois P. Heinz, <a href="/A208570/b208570.txt">Table of n, a(n) for n = 1..10000</a>
%F A208570 From _Robert Israel_, May 20 2015: (Start)
%F A208570 a(n) = lcm(n, A007978(n)).
%F A208570 For primes p let nu_p(n) be the p-adic order of n.
%F A208570 a(n) = p * n where p is the prime that minimizes p^(1+nu_p(n)). (End)
%e A208570 a(6) = 12 because the divisors of 6 are 1,2,3,6; 4 is the smallest number not a divisor of 6; the LCM of 6 and 4 is 12.
%p A208570 a:= proc(n) local t;
%p A208570       for t from 2 do
%p A208570         if irem (n, t)<>0 then return ilcm(t, n) fi
%p A208570       od
%p A208570     end:
%p A208570 seq(a(n), n=1..100); # _Alois P. Heinz_, Mar 13 2012
%t A208570 Table[LCM[n, Min[Complement[Range[n + 1], Divisors[n]]]], {n, 61}] (* _Ivan Neretin_, May 20 2015 *)
%o A208570 (Haskell)
%o A208570 a208570 n = lcm n $ a007978 n  -- _Reinhard Zumkeller_, May 22 2015
%o A208570 (PARI) a(n) = {my(k=2); while(!(n % k), k++); lcm(n, k); } \\ _Michel Marcus_, Mar 13 2018
%Y A208570 Cf. A007978.
%Y A208570 Cf. A258115.
%K A208570 nonn
%O A208570 1,1
%A A208570 _J. Lowell_, Feb 28 2012
%E A208570 More terms from _Alois P. Heinz_, Mar 13 2012