A335114 a(n) is the greatest k > 0 such that Sum_{j=1..n} j*(-k)^j/(k+n) is integer, for n > 1 and a(n) != n + 1.

8, 69, 864, 13460, 245664, 5134283, 120961664, 3172973814, 91735537200, 2898687320177, 99396054701280, 3676223870321288, 145888302945326144, 6183540678620338455, 278807536726516683264, 13325206564150591272362, 672921671625708650943696, 35804449718312525179171229

Offset

2,1

Comments

a(n) represents the greatest integer solution of the equation (- k + 2*k^2 - ... +/- (n - 1)*k^(n - 1) -/+ n*k^n)/(k + n) = m, where m is any integer, while a(n) is not equal to the trivial solution n + 1 (i.e., a(1) != 2 does not exist even if (- 2)/(2 - 1) = - 2).

If we introduce the additional constraint m>0, then the corresponding sequence is 8, 2, 864, ...

Links

Table of n, a(n) for n=2..19.

Formula

a(n) = A335112(n) + 2*n.

Example

For n = 3, a(3) is the largest integer x > 0 such that f(k) = - 3k^3 + 2k^2 - k)/(k - 3) is an integer. Since f(k) is integer for k = 1, 2, 4, 5, 6, 9, 14, 25, 36, 69, we have a(3) = 69.

Crossrefs

Cf. A335112, A335113.

Sequence in context: A317096 A327606 A336951 * A226597 A209074 A124152

Adjacent sequences: A335111 A335112 A335113 * A335115 A335116 A335117

Keyword

nonn

Author

Marco Ripà, May 23 2020

Status

approved