A092990 Least product of the partitions of n into two parts with maximal tau value: let n = a+b be a partition of n, then a(n) = a*b such that tau(a*b) is maximal.

1, 2, 4, 6, 8, 12, 12, 18, 24, 24, 36, 36, 48, 36, 60, 60, 72, 60, 84, 90, 120, 120, 144, 144, 120, 180, 180, 180, 216, 240, 240, 252, 240, 300, 180, 336, 360, 360, 336, 420, 360, 420, 420, 504, 360, 420, 540, 360, 504, 540, 420, 360, 720, 600, 720, 540, 840, 840

Offset: 2

Author

Amarnath Murthy, Mar 28 2004

Keywords

• nonn

Examples

			a(9) = 18 as 18 = 3 * 6 has 6 divisors. 20 = 4 * 5 also has 6 divisors, but 20 > 18.
		

Links

• David A. Corneth, Table of n, a(n) for n = 2..10001

Crossrefs

Cf. A092991.

Cf. A000005.

Programs

PARI

a(n) = {my(res = n-1, r = numdiv(n-1)); for(i = 2, (n+1)\2, c = numdiv(i*(n-i)); if(c > r, r = c; res = i*(n-i); ) ); res } \\ David A. Corneth, Dec 27 2020

Extensions

Corrected and extended by Franklin T. Adams-Watters, Jun 14 2006