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

1,3

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A187203, A187205, A187207, A187208.

Sequence in context: A201777 A096189 A010464 * A006579 A227906 A366974

Adjacent sequences: A187206 A187207 A187208 * A187210 A187211 A187212

Keyword

nonn

Author

Omar E. Pol, Aug 04 2011

Status

approved