A235268 Least integer k > n such that n*k/(n+k) is an integer, or 0 if no such k exists.

1, 0, 0, 6, 12, 20, 12, 42, 24, 18, 15, 110, 24, 156, 35, 30, 48, 272, 36, 342, 30, 28, 99, 506, 40, 100, 143, 54, 70, 812, 45, 930, 96, 66, 255, 140, 45, 1332, 323, 78, 60, 1640, 56, 1806, 77, 90, 483, 2162, 80, 294, 75, 102, 117, 2756, 108, 66, 140, 114, 783

Offset: 0

Author

Alex Ratushnyak, Jan 05 2014

Keywords

• nonn

Examples

			a(3) = 6 because 6 is the smallest k > 3 such that k*3/(k+3) is an integer.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A063427.

Programs

Mathematica

a[0]=1; a[n_] := Block[{k,s,x}, s = Reduce[k*n/(k+n) == x && k>n, {k,x}, Integers]; If[s === False, 0, Min[k /. List@ ToRules@s]]]; a/@Range[0,100] (* Giovanni Resta, Jan 20 2014 *)

PARI

a(n)=my(k=n+1);while((n*k)%(n+k)!=0,k=k+1);k \\ Ralf Stephan, Jan 15 2014

Formula

For prime p, a(p) = p*(p-1) = A002378(p-1). - Ralf Stephan, Jan 15 2014