A092988 Least number k < n such that n*k has the maximum number of divisors.

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

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