A192488 Numbers that set records for number of divisors of n(n-1).

2, 3, 4, 6, 9, 15, 16, 21, 36, 64, 81, 100, 105, 196, 225, 385, 441, 561, 936, 1225, 1540, 2016, 2080, 5265, 5985, 12376, 21736, 41041, 78625, 123201, 126225, 156520, 176176, 201825, 313600, 338625, 395200, 453376, 638001, 1154440, 1890945, 2203201, 2697696, 2756160, 4921840, 6969600

Offset: 1

Author

J. Lowell, Jul 02 2011

Keywords

• nonn

Comments

Places of records in A092517.

Bases for which it is easy to find divisibility rules for many numbers in those bases; in base 64 the final digit rule works for 1,2,4,8,16,32,64 and the add the digits rule works for 1,3,7,9,21,63.

Examples

			6 qualifies because 6*5=30 has 8 divisors, more than any smaller number of the form n(n-1).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..61

Programs

Mathematica

DeleteDuplicates[Table[{n,DivisorSigma[0,n(n-1)]},{n,2,7*10^6}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, May 25 2024 *)

PARI

r=0;t1=1;for(n=2,1e8,t2=numdiv(n);if(t1*t2>r,r=t1*t2;print1(n", "));t1=t2) \\ Charles R Greathouse IV, Jul 03 2011