A283074 Numbers k such that the central binomial coefficient C(2*k,k) is divisible by k^5.

1, 84331608790, 94482127740, 164273806200, 438726722148, 541278246600, 549361342530, 808172086449, 912226745430, 959218287720, 1017676553985, 1017868271175, 1078659050256, 1286556180525, 1418394308100, 1475851476960, 1489765799610, 1535790227400, 1562434592400, 1642639268270

Offset

1,2

Comments

Equivalently, numbers k such that the k-th Catalan number C(2*k,k)/(k+1) is divisible by k^5.

The asymptotic density of this sequence is 2.83248121476... * 10^(-10) (Ford and Konyagin, 2021). - Amiram Eldar, Jan 26 2021

Links

Giovanni Resta, Table of n, a(n) for n = 1..123 (terms < 10^13).

Kevin Ford and Sergei Konyagin, Divisibility of the central binomial coefficient binomial(2n, n), Trans. Amer. Math. Soc., Vol. 374, No. 2 (2021), pp. 923-953; arXiv preprint, arXiv:1909.03903 [math.NT], 2019-2020.

Example

The central binomial coefficient C(2*84331608790,84331608790) is divisible by 84331608790^5.

Crossrefs

Cf. A000108, A000984, A014847, A121943, A282163, A282346, A283073, A282672.

Sequence in context: A209598 A233608 A115538 * A233600 A164727 A164728

Adjacent sequences: A283071 A283072 A283073 * A283075 A283076 A283077

Keyword

nonn

Author

Lucian Craciun, Feb 28 2017

Extensions

a(3)-a(20) from Giovanni Resta, Mar 03 2017

Status

approved