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A092988
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Least number k < n such that n*k has the maximum number of divisors.
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2
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1, 2, 3, 4, 4, 6, 6, 8, 6, 6, 10, 12, 12, 12, 15, 12, 10, 12, 18, 20, 18, 12, 15, 24, 24, 20, 15, 24, 28, 24, 30, 20, 30, 24, 35, 36, 30, 20, 36, 36, 40, 36, 30, 28, 30, 36, 35, 48, 36, 40, 45, 48, 40, 48, 45, 40, 30, 48, 42, 60, 60, 40, 45, 48, 60, 60, 60, 60, 36, 60, 70, 60, 60
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OFFSET
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2,2
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LINKS
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EXAMPLE
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a(14) = 6 as 14*6 = 84 = 2^2*3*7 has 12 divisors, though 14*9 = 126 = 3^2*2*7 also has 12 divisors but 9 > 6.
a(15) = 12 as 180 has 18 divisors 15*14 = 210 has 16 divisors.
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MATHEMATICA
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Do[x = y = 0; For[k = 1, k < n, k++, d = Length[Divisors[n*k]]; If[d > x, x = d; y = k]]; Print[y], {n, 2, 50}] (* Ryan Propper, Jul 25 2005 *)
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PROG
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(PARI) a(n) = {my(res = 1, r = numdiv(n)); for(i = 2, n - 1, c = numdiv(i*n); if(c > r, r = c; res = i); ); res } \\ David A. Corneth, Dec 27 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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