cp's OEIS Frontend

A192286 Antiharmonic numbers using anti-divisors: numbers n such that sigma*(n) divides sigma*_2(n), where sigma*(n) is the sum of anti-divisors of n and sigma*_2(n) the sum of squares of anti-divisors of n.

%I A192286 #13 May 07 2014 09:17:03
%S A192286 3,4,6,9,36,54,96,216,576,1212,1296,1582,2171,3129,3599,26847,45914,
%T A192286 69984,76393,91013,137173,176678,182559,183087,236196,393216,497664,
%U A192286 3823898,28697814,31850496,46572031,47992961,83951616,84934656,95969521,126310141,472250381
%N A192286 Antiharmonic numbers using anti-divisors: numbers n such that sigma*(n) divides sigma*_2(n), where sigma*(n) is the sum of anti-divisors of n and sigma*_2(n) the sum of squares of anti-divisors of n.
%F A192286 Like A020487 but using anti-divisors.
%F A192286 4, 9, 36, 576, 1296, etc. are antiharmonic both with divisors and anti-divisors.
%e A192286 Anti-divisors of 1212 are 5, 8, 24, 25, 97, 485, 808 and their sum is 1452. The sum of the squares of anti-divisors is 898788 and 898788/1452=619.
%p A192286 with(numtheory);
%p A192286 P:=proc(n)
%p A192286 local a,b,i,k;
%p A192286 for i from 3 to n do
%p A192286   a:=0; b:=0;
%p A192286   for k from 2 to i-1 do
%p A192286     if abs((i mod k)- k/2) < 1 then a:=a+k; b:=b+k^2; fi;
%p A192286   od;
%p A192286   if trunc(b/a)=b/a then print(i); fi;
%p A192286 od;
%p A192286 end:
%p A192286 P(200000);
%Y A192286 Cf. A020487, A066272.
%K A192286 nonn
%O A192286 1,1
%A A192286 _Paolo P. Lava_, Jul 28 2011
%E A192286 a(22)-a(37) from _Donovan Johnson_, Sep 22 2011