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

1,1

Comments

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

Links

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

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)

Example

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.

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 *)

Prog

(Haskell)
a208570 n = lcm n $ a007978 n  -- Reinhard Zumkeller, May 22 2015
(PARI) a(n) = {my(k=2); while(!(n % k), k++); lcm(n, k); } \\ Michel Marcus, Mar 13 2018

Crossrefs

Cf. A007978.

Cf. A258115.

Sequence in context: A306925 A134466 A062562 * A106832 A129902 A350631

Adjacent sequences: A208567 A208568 A208569 * A208571 A208572 A208573

Keyword

nonn

Author

J. Lowell, Feb 28 2012

Extensions

More terms from Alois P. Heinz, Mar 13 2012

Status

approved