A285120 Min(|d(k+1-i) - d(i)|, for i = 1..k), where d(1),..,d(k) are the divisors of n(n+1)/2.

0, 2, 1, 3, 2, 4, 3, 0, 4, 6, 5, 7, 6, 8, 2, 9, 8, 10, 9, 1, 10, 12, 11, 5, 12, 14, 3, 15, 14, 16, 15, 2, 16, 18, 9, 19, 18, 20, 4, 21, 20, 22, 21, 3, 22, 24, 23, 14, 0, 26, 5, 27, 26, 12, 9, 4, 28, 30, 29, 31, 30, 32, 6, 12, 16, 34, 33, 5, 34, 36, 35, 37

Offset: 1

Author

Clark Kimberling, Apr 11 2017

Keywords

• nonn
• easy

Examples

			7(7+1)/2 = 28 has divisors 1,2,4,7,14,28, so that k=6 and d(k+1-i) - d(i) ranges through {-27,-12,-3,3,12,27}, so that a(7) = 3.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A002378, A056737.

Programs

Mathematica

f[n_] := f[n] = n(n+1)/2;
Table[Divisors[f[n]] - Reverse[Divisors[f[n]]], {n, 1, 10}]
Table[Min[Abs[Divisors[f[n]] - Reverse[Divisors[f[n]]]]], {n, 1, 100}]

Formula

a(n)=A056737(A000217(n)).