A285121 Min(|d(k+1-i) - d(i)|, for i = 1..k), where d(1),..,d(k) are the divisors of n*(n+1)*(n+2)/6.

0, 0, 3, 1, 2, 1, 5, 2, 4, 9, 9, 12, 22, 8, 14, 10, 32, 8, 3, 9, 54, 2, 4, 2, 20, 11, 5, 12, 114, 18, 26, 20, 8, 1, 31, 35, 210, 9, 48, 58, 244, 68, 19, 17, 26, 90, 90, 0, 56, 40, 115, 3, 6, 3, 36, 51, 492, 91, 173, 89, 34, 25, 2, 12, 192, 81, 257, 8

Offset

1,3

Links

Clark Kimberling, Table of n, a(n) for n = 1..9998

Formula

a(n) = A056737(A000292(n)).

Example

6(6+1)(6+2)/6 = 56 has divisors 1,2,4,7,8,14,28,56, so that k=8 and d(k+1-i) - d(i) ranges through {-55, -26, -10, -1, 1, 10, 26, 55}, so that a(6) = 1.

Mathematica

f[n_] := f[n] = n(n+1)(n+2)/6;
Table[Divisors[f[n]] - Reverse[Divisors[f[n]]], {n, 1, 10}]
Table[Min[Abs[Divisors[f[n]] - Reverse[Divisors[f[n]]]]], {n, 1, 100}]

Crossrefs

Cf. A000292, A002378, A056737.

Sequence in context: A059807 A214208 A279965 * A295935 A318323 A366803

Adjacent sequences: A285118 A285119 A285120 * A285122 A285123 A285124

Keyword

nonn,easy

Author

Clark Kimberling, Apr 11 2017

Extensions

Two extraneous 0's removed by Pontus von Brömssen, Jul 15 2023

Status

approved