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.

3, 4, 6, 9, 36, 54, 96, 216, 576, 1212, 1296, 1582, 2171, 3129, 3599, 26847, 45914, 69984, 76393, 91013, 137173, 176678, 182559, 183087, 236196, 393216, 497664, 3823898, 28697814, 31850496, 46572031, 47992961, 83951616, 84934656, 95969521, 126310141, 472250381

Offset: 1

Author

Paolo P. Lava, Jul 28 2011

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A020487, A066272.

Programs

Maple

with(numtheory);
P:=proc(n)
local a,b,i,k;
for i from 3 to n do
  a:=0; b:=0;
  for k from 2 to i-1 do
    if abs((i mod k)- k/2) < 1 then a:=a+k; b:=b+k^2; fi;
  od;
  if trunc(b/a)=b/a then print(i); fi;
od;
end:
P(200000);

Formula

Like A020487 but using anti-divisors.

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

Extensions

a(22)-a(37) from Donovan Johnson, Sep 22 2011