A208570 LCM of n and smallest nondivisor of n.

2, 6, 6, 12, 10, 12, 14, 24, 18, 30, 22, 60, 26, 42, 30, 48, 34, 36, 38, 60, 42, 66, 46, 120, 50, 78, 54, 84, 58, 60, 62, 96, 66, 102, 70, 180, 74, 114, 78, 120, 82, 84, 86, 132, 90, 138, 94, 240, 98, 150, 102, 156, 106, 108, 110, 168, 114, 174, 118, 420, 122

Offset: 1

Author

J. Lowell, Feb 28 2012

Keywords

• nonn

Comments

a(n) = 2*n for all odd numbers.

Examples

			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.
		

Links

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

Crossrefs

Cf. A007978.

Cf. A258115.

Programs

Haskell

a208570 n = lcm n $ a007978 n  -- Reinhard Zumkeller, May 22 2015

Maple

a:= proc(n) local t;
      for t from 2 do
        if irem (n, t)<>0 then return ilcm(t, n) fi
      od
    end:
seq(a(n), n=1..100); # Alois P. Heinz, Mar 13 2012

Mathematica

Table[LCM[n, Min[Complement[Range[n + 1], Divisors[n]]]], {n, 61}] (* Ivan Neretin, May 20 2015 *)

PARI

a(n) = {my(k=2); while(!(n % k), k++); lcm(n, k); } \\ Michel Marcus, Mar 13 2018

Formula

From Robert Israel, May 20 2015: (Start)

a(n) = lcm(n, A007978(n)).

For primes p let nu_p(n) be the p-adic order of n.

a(n) = p * n where p is the prime that minimizes p^(1+nu_p(n)). (End)

Extensions

More terms from Alois P. Heinz, Mar 13 2012