A174554 Smallest k > 2 such that 2|k, 3|k+1, 4|k+2,..., n|k+n-2.

4, 8, 14, 62, 62, 422, 842, 2522, 2522, 27722, 27722, 360362, 360362, 360362, 720722, 12252242, 12252242, 232792562, 232792562, 232792562, 232792562, 5354228882, 5354228882, 26771144402, 26771144402, 80313433202, 80313433202

Offset: 2

Author

Michel Lagneau, Mar 22 2010

Keywords

• nonn

Comments

We solve the system of n+1 equations : k==2 (mod 2), k==2 (mod 3),...,k==2 (mod n), and then the solutions are k== 2 mod (lcm(2,3,4,...,n)) where lcm(k) is the least common multiple of{1, 2, ..., k}(A003418) .

Examples

			a(2) = 4 because 2|4;
a(3) = 8 because 2|8 and 3|9;
a(4) = 14 because 2|14, 3|15 and 4|16;
a(5) = 62 because 2|62, 3|63, 4|64 and 5|65;
a(6) = 62 because 2|62, 3|63, 4|64, 5|65 and 6|66.
		

Links

• Bakir Farhi, An identity involving the least common multiple of binomial coefficients and its application, arXiv:0906.2295 [math.NT], 2009.
• Bakir Farhi, An identity involving the least common multiple of binomial coefficients and its application, Amer. Math. Monthly, 116 (2009), 836-839.
• Eric Weisstein's World of Mathematics, Least Common Multiple

Crossrefs

Cf. A002944, A003990, A051173, A000793, A003418, A048691.

Programs

Maple

with(numtheory):q:=2:for k from 2 to 100 do :q1:= lcm(q,k):q2 :=2+q1 :print(q2): q :=q1 :od :

Formula

a(n) = 2 + lcm(2,3,4,...,n) = A003418(n) + 2.