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A335112 a(n) is the greatest k > 0 such that Sum_{j=1..n} j*k^j/(k+n) is integer, for n > 1. 2
4, 63, 856, 13450, 245652, 5134269, 120961648, 3172973796, 91735537180, 2898687320155, 99396054701256, 3676223870321262, 145888302945326116, 6183540678620338425, 278807536726516683232, 13325206564150591272328, 672921671625708650943660, 35804449718312525179171191 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) represents the greatest integer solution of the (degree n polynomial) equation (k + 2*k^2 + ... + (n - 1)*k^(n - 1) + n*k^n)/(k + n) = m, where m is any positive integer.

LINKS

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

FORMULA

a(n) = abs(Sum_{j=1..n} j*(-n)^j) - n = n*abs(((n+1)*(-n)^n+(-n)^(n+2)-1)/(n+1)^2) - n. - Giovanni Resta, May 24 2020

EXAMPLE

For n = 4, a(4) is the largest integer k > 0 such that f(k) = 4k^4 + 3k^3 + 2k^2 + k)/(k + 4) is an integer. Since f(k) is integer for k = 1, 6, 16, 39, 82, 168, 211, 426, 856, we have a(4) = 856.

MATHEMATICA

a[n_] := -n + Abs@ Sum[j (-n)^j, {j, n}]; a /@ Range[2, 19] (* Giovanni Resta, May 24 2020 *)

CROSSREFS

Cf. A335113, A335114.

Sequence in context: A094323 A286438 A224249 * A227619 A177788 A293860

Adjacent sequences:  A335109 A335110 A335111 * A335113 A335114 A335115

KEYWORD

nonn

AUTHOR

Marco Ripà, May 23 2020

EXTENSIONS

More terms from Giovanni Resta, May 24 2020

STATUS

approved

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Last modified June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)