cp's OEIS Frontend

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

%I A187215 #55 May 20 2016 04:13:48
%S A187215 1,4,6,11,10,21,14,26,25,31,22,52,26,45,54,57,34,82,38,82,72,73,46,
%T A187215 119,71,87,90,108,58,161,62,120,108,115,134,181,74,129,126,193,82,221,
%U A187215 86,172,218,157,94,252,141,190,162,204,106,285,202,233
%N A187215 Sum of the elements of the absolute difference table of the divisors of n.
%C A187215 First differs from A273103 at a(14). - _Omar E. Pol_, May 15 2016
%H A187215 Alois P. Heinz, <a href="/A187215/b187215.txt">Table of n, a(n) for n = 1..10000</a>
%F A187215 a(n) = 2n, if n is prime.
%F A187215 a(2^k) = A125128(k+1), k >= 0. - _Omar E. Pol_, May 15 2016
%e A187215 For n = 14 the divisors of 14 are 1, 2, 7, 14, and the absolute difference triangle of the divisors is
%e A187215 1 . 2 . 7 . 14
%e A187215 . 1 . 5 . 7
%e A187215 . . 4 . 2
%e A187215 . . . 2
%e A187215 The sum of all elements of the triangle is 1 + 2 + 7 + 14 + 1 + 5 + 7 + 4 + 2 + 2 = 45, so a(14) = 45.
%p A187215 with(numtheory):
%p A187215 DD:= l-> [seq(abs(l[i]-l[i-1]), i=2..nops(l))]:
%p A187215 a:= proc(n) local l;
%p A187215       l:= sort([divisors(n)[]], `>`);
%p A187215       add(j, j=[seq((DD@@i)(l)[], i=0..nops(l)-1)]);
%p A187215     end:
%p A187215 seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 02 2011
%t A187215 Table[Total@ Flatten@ NestWhileList[Abs@ Differences@ # &, Divisors@ n, Length@ # > 1 &], {n, 56}] (* _Michael De Vlieger_, May 18 2016 *)
%Y A187215 Row sums of triangle A187207.
%Y A187215 Cf. A000203, A056538, A187203, A187209, A273103.
%K A187215 nonn,easy
%O A187215 1,2
%A A187215 _Omar E. Pol_, Aug 02 2011
%E A187215 More terms from _Alois P. Heinz_, Aug 02 2011
%E A187215 Edited by _Omar E. Pol_, May 19 2016