

A174554


Smallest k > 2 such that 2k, 3k+1, 4k+2,..., nk+n2.


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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), 836839.
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 24;
a(3) = 8 because 28 and 39;
a(4) = 14 because 214, 315 and 416;
a(5) = 62 because 262, 363, 464 and 565;
a(6) = 62 because 262, 363, 464, 565 and 666.


MAPLE

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


CROSSREFS

Cf. A002944, A003990, A051173, A000793, A003418, A048691.
Sequence in context: A188575 A324585 A242519 * A272048 A112312 A076343
Adjacent sequences: A174551 A174552 A174553 * A174555 A174556 A174557


KEYWORD

nonn


AUTHOR

Michel Lagneau, Mar 22 2010


STATUS

approved



