A174554 - OEIS

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

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OFFSET

2,1

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) .

LINKS

Table of n, a(n) for n=2..28.

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

FORMULA

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

EXAMPLE

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;