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 A092988 Least number k < n such that n*k has the maximum number of divisors. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS David A. Corneth, Table of n, a(n) for n = 2..10000 EXAMPLE 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A092989. Sequence in context: A262265 A227683 A321166 * A304575 A296421 A138768 Adjacent sequences: A092985 A092986 A092987 * A092989 A092990 A092991 KEYWORD nonn AUTHOR Amarnath Murthy, Mar 28 2004 EXTENSIONS 35 more terms from Ryan Propper, Jul 25 2005 More terms from David Wasserman, Aug 22 2006 STATUS approved

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Last modified December 7 17:25 EST 2022. Contains 358668 sequences. (Running on oeis4.)