A172520 Triangle in which row n gives the number of divisors of numbers in the range n to n+k for k=0..n-1.

1, 2, 3, 2, 4, 5, 3, 4, 6, 7, 2, 5, 6, 8, 9, 4, 5, 7, 8, 10, 11, 2, 5, 7, 9, 10, 12, 13, 4, 6, 8, 9, 11, 12, 14, 15, 3, 6, 7, 10, 11, 13, 14, 16, 17, 4, 5, 9, 10, 12, 13, 15, 16, 18, 19, 2, 7, 8, 10, 12, 14, 15, 17, 18, 20, 21, 6, 7, 9, 11, 13, 14, 16, 17, 19, 20, 22, 23, 2, 5, 8, 11, 12

Offset

1,2

Comments

Row n begins with the number of divisors of n and ends with 2n-1. Observe that the reverse of row n starts 2n-1, 2n-2, 2n-4, 2n-5,...; that is, 2n-r where r is in A001651, numbers not divisible by 3. Why?

Links

T. D. Noe, Rows n=1..100, flattened

Example

For n=5, we have 2 numbers that divide 5 (namely, 1 and 5), 5 numbers that divide numbers in the range [5,6] (namely, 1, 2, 3, 5 and 6), 6 divisors that divide numbers in the range [5,7] (namely, 1, 2, 3, 5, 6 and 7), 8 divisors that divide numbers in the range [5,8] (namely, all numbers from 1 to 8), and 9 divisors that divide numbers in the range [5,9] (namely, all numbers from 1 to 9). Hence row 5 is 2, 5, 6, 8, 9.

Mathematica

Flatten[Table[Length[Union[Flatten[Divisors[Range[n, n+k]]]]], {n, 50}, {k, 0, n-1}]]

Crossrefs

Sequence in context: A252371 A275817 A286533 * A290094 A285904 A285714

Adjacent sequences: A172517 A172518 A172519 * A172521 A172522 A172523

Keyword

nonn,tabl

Author

T. D. Noe, Feb 06 2010

Status

approved