A172520 - OEIS

%I #5 Mar 30 2012 17:22:55

%S 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,

%T 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,

%U 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

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

%C 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?

%H T. D. Noe, <a href="/A172520/b172520.txt">Rows n=1..100, flattened</a>

%e 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.

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

%K nonn,tabl

%O 1,2

%A _T. D. Noe_, Feb 06 2010