A187209 Sum of all terms of triangle of absolute differences of the divisors of n.

0, 1, 2, 4, 4, 9, 6, 11, 12, 13, 10, 24, 12, 21, 30, 26, 16, 43, 18, 40, 40, 37, 22, 59, 40, 45, 50, 52, 28, 89, 30, 57, 60, 61, 86, 90, 36, 69, 70, 103, 40, 125, 42, 88, 140, 85, 46, 128, 84, 97, 90, 106, 52, 165, 130, 113, 100, 109, 58, 201

Offset: 1

Author

Omar E. Pol, Aug 04 2011

Keywords

• nonn

Comments

Note that if n is prime then a(n) = n - 1.

Examples

			a(10) = 13 because the divisors of 10 are 1, 2, 5, 10; the triangle of absolute differences is
1, 3, 5;
. 2, 2;
.   0;
and the sum of the terms of triangle is 1+3+5+2+2+0 = 13.
		

Crossrefs

Cf. A187203, A187205, A187207, A187208.

Programs

Mathematica

Table[Total[Flatten[NestList[Abs[Differences[#]]&,Differences[Divisors[ n]], DivisorSigma[0,n]-1]]],{n,60}] (* Harvey P. Dale, Aug 10 2011 *)

Formula

a(n) = A187215(n) - A000203(n).