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A187215
Sum of the elements of the absolute difference table of the divisors of n.
11
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
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.
Sequence in context: A129235 A012903 A273103 * A365647 A322577 A013018
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