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A282672 Numbers k such that the central binomial coefficient C(2*k,k) is divisible by k^6. 7
1, 1138842118714300, 1605078397568386, 1785922862964240, 1878157384495600, 2020105305316098, 2055406015517400, 2071857393746595, 2310442996851990, 2450253379658700, 2513216312053944, 2966830431558840, 2990886595291870, 3228082757486928, 3318987930069240 (list; graph; refs; listen; history; text; internal format)



Also numbers k such that the k-th Catalan number C(2*k,k)/(k+1) is divisible by k^6.


Giovanni Resta, Table of n, a(n) for n = 1..97

Kevin Ford, Sergei Konyagin, Divisibility of the central binomial coefficient binomial(2n, n), arXiv:1909.03903 [math.NT], 2019.


Let E(n,p) be the exponent of the prime p in the factorization of n. Note that E(n!,p) can be easily found with Legendre's formula without computing n!. Then, t = 1138842118714300 is in the sequence because for each prime p dividing t we have E(C(2*t,t),p) = E((2*t)!,p) - 2*E(t!,p) >= 6*E(t,p).


Cf. A000108, A000984, A014847, A121943, A282163, A282346, A283073, A283074.

Sequence in context: A172607 A235167 A095431 * A072719 A185433 A134692

Adjacent sequences:  A282669 A282670 A282671 * A282673 A282674 A282675




Giovanni Resta, Mar 16 2017



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Last modified November 27 08:53 EST 2020. Contains 338679 sequences. (Running on oeis4.)