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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A173278 A173289 A096824 * A089797 A081237 A022159

Adjacent sequences: A192485 A192486 A192487 * A192489 A192490 A192491

Keyword

nonn

Author

J. Lowell, Jul 02 2011

Status

approved