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 A292441 Largest m such that m^2 divides A000984(n). 2
 1, 1, 1, 2, 1, 6, 2, 2, 3, 2, 2, 2, 2, 10, 30, 12, 3, 6, 10, 10, 6, 2, 2, 60, 30, 42, 42, 28, 2, 4, 4, 4, 21, 14, 14, 6, 2, 2, 10, 140, 14, 126, 6, 60, 90, 12, 84, 84, 210, 30, 18, 12, 6, 36, 4, 4, 6, 4, 4, 12, 12, 132, 132, 440, 55, 330, 10, 10, 90, 30, 30, 180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) is the product of p^floor(m(n,p)/2) over primes p sqrt(n/5) if n >= 2082. In particular a(n) -> infinity as n -> infinity. - Robert Israel, Sep 18 2017 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 A. Granville and O. Ramaré, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika 43 (1996), 73-107, [DOI]. Eric Weisstein's World of Mathematics, Erdős Squarefree Conjecture Wikipedia, Kummer's theorem FORMULA a(n) > 1 for n > 4. a(n) = A000188(A000984(n)). - Robert Israel, Sep 17 2017 EXAMPLE binomial(10,5)/7           =  252/7   = 36 = a(5)^2. binomial(12,6)/(3*7*11)    =  924/231 =  4 = a(6)^2. binomial(14,7)/(2*3*11*13) = 3432/858 =  4 = a(7)^2. MAPLE A000188:= n -> mul(t[1]^floor(t[2]/2), t = ifactors(n)[2]): seq(A000188(binomial(2*n, n)), n=0..100); # Robert Israel, Sep 17 2017 CROSSREFS Cf. A000188, A000984, A006530, A292442. Sequence in context: A157392 A134134 A222005 * A198870 A050457 A195441 Adjacent sequences:  A292438 A292439 A292440 * A292442 A292443 A292444 KEYWORD nonn AUTHOR Seiichi Manyama, Sep 16 2017 STATUS approved

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Last modified August 14 06:01 EDT 2018. Contains 313748 sequences. (Running on oeis4.)