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
Examples
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.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
Programs
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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 *)
Formula
a(n) = 2n, if n is prime.
a(2^k) = A125128(k+1), k >= 0. - Omar E. Pol, May 15 2016
Extensions
More terms from Alois P. Heinz, Aug 02 2011
Edited by Omar E. Pol, May 19 2016
Comments