A285119 Min(|d(k+1-i) - d(i)|, for i = 1..k), where d(1)..d(k) are the divisors of n^3.

0, 2, 6, 0, 20, 6, 42, 16, 0, 15, 110, 12, 156, 7, 30, 0, 272, 9, 342, 20, 84, 33, 506, 20, 0, 65, 162, 84, 812, 30, 930, 128, 176, 153, 70, 0, 1332, 209, 182, 6, 1640, 42, 1806, 110, 132, 345, 2162, 96, 0, 250, 170, 78, 2756, 162, 330, 56, 152, 609, 3422

Offset: 1

Author

Clark Kimberling, Apr 11 2017

Keywords

• nonn
• look
• easy

Comments

a(n) = 0 if and only if n is a square (A000290).

Examples

			3^3 = 27 has divisors 1,3,9,27, so that k=4 and d(k+1-i) - d(i) ranges through {-26,-6,6,27}, so that a(3) = 6.
		

Links

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

Crossrefs

Cf. A002378, A000578, A056737.

Programs

Mathematica

f[n_] := f[n] = n^3; Table[Divisors[f[n]] - Reverse[Divisors[f[n]]], {n, 1, 10}]
Table[Min[Abs[Divisors[f[n]] - Reverse[Divisors[f[n]]]]], {n, 1, 100}]

PARI

a(n) = my(d=divisors(n^3)); vecmin(apply(abs, d - Vecrev(d))); \\ Michel Marcus, Feb 22 2021

Formula

a(n) = A056737(A000578(n)).