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 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. 2

%I

%S 1,2,4,6,8,12,12,18,24,24,36,36,48,36,60,60,72,60,84,90,120,120,144,

%T 144,120,180,180,180,216,240,240,252,240,300,180,336,360,360,336,420,

%U 360,420,420,504,360,420,540,360,504,540,420,360,720,600,720,540,840,840

%N 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.

%H David A. Corneth, <a href="/A092990/b092990.txt">Table of n, a(n) for n = 2..10001</a>

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

%o (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

%Y Cf. A092991.

%Y Cf. A000005.

%K nonn

%O 2,2

%A _Amarnath Murthy_, Mar 28 2004

%E Corrected and extended by _Franklin T. Adams-Watters_, Jun 14 2006

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Last modified January 27 10:15 EST 2023. Contains 359838 sequences. (Running on oeis4.)