A192286 - OEIS

%I #13 May 07 2014 09:17:03

%S 3,4,6,9,36,54,96,216,576,1212,1296,1582,2171,3129,3599,26847,45914,

%T 69984,76393,91013,137173,176678,182559,183087,236196,393216,497664,

%U 3823898,28697814,31850496,46572031,47992961,83951616,84934656,95969521,126310141,472250381

%N 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 Like A020487 but using anti-divisors.

%F 4, 9, 36, 576, 1296, etc. are antiharmonic both with divisors and anti-divisors.

%e 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 with(numtheory);

%p P:=proc(n)

%p local a,b,i,k;

%p for i from 3 to n do

%p   a:=0; b:=0;

%p   for k from 2 to i-1 do

%p     if abs((i mod k)- k/2) < 1 then a:=a+k; b:=b+k^2; fi;

%p   od;

%p   if trunc(b/a)=b/a then print(i); fi;

%p od;

%p end:

%p P(200000);

%Y Cf. A020487, A066272.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Jul 28 2011

%E a(22)-a(37) from _Donovan Johnson_, Sep 22 2011