A292441 Largest m such that m^2 divides A000984(n).
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
Offset: 0
Keywords
Examples
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.
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
Programs
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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
Formula
a(n) > 1 for n > 4.
Comments