A187215 Sum of the elements of the absolute difference table of the divisors of n.

1, 4, 6, 11, 10, 21, 14, 26, 25, 31, 22, 52, 26, 45, 54, 57, 34, 82, 38, 82, 72, 73, 46, 119, 71, 87, 90, 108, 58, 161, 62, 120, 108, 115, 134, 181, 74, 129, 126, 193, 82, 221, 86, 172, 218, 157, 94, 252, 141, 190, 162, 204, 106, 285, 202, 233

Offset

1,2

Comments

First differs from A273103 at a(14). - Omar E. Pol, May 15 2016

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2n, if n is prime.

a(2^k) = A125128(k+1), k >= 0. - Omar E. Pol, May 15 2016

Example

For n = 14 the divisors of 14 are 1, 2, 7, 14, and the absolute difference triangle of the divisors is
1 . 2 . 7 . 14
. 1 . 5 . 7
. . 4 . 2
. . . 2
The sum of all elements of the triangle is 1 + 2 + 7 + 14 + 1 + 5 + 7 + 4 + 2 + 2 = 45, so a(14) = 45.

Maple

with(numtheory):
DD:= l-> [seq(abs(l[i]-l[i-1]), i=2..nops(l))]:
a:= proc(n) local l;
      l:= sort([divisors(n)[]], `>`);
      add(j, j=[seq((DD@@i)(l)[], i=0..nops(l)-1)]);
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 02 2011

Mathematica

Table[Total@ Flatten@ NestWhileList[Abs@ Differences@ # &, Divisors@ n, Length@ # > 1 &], {n, 56}] (* Michael De Vlieger, May 18 2016 *)

Crossrefs

Row sums of triangle A187207.

Cf. A000203, A056538, A187203, A187209, A273103.

Sequence in context: A129235 A012903 A273103 * A365647 A322577 A013018

Adjacent sequences: A187212 A187213 A187214 * A187216 A187217 A187218

Keyword

nonn,easy

Author

Omar E. Pol, Aug 02 2011

Extensions

More terms from Alois P. Heinz, Aug 02 2011

Edited by Omar E. Pol, May 19 2016

Status

approved