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

1,1

Links

Table of n, a(n) for n=1..37.

Formula

Like A020487 but using anti-divisors.

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

Example

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.

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);

Crossrefs

Cf. A020487, A066272.

Sequence in context: A350741 A191699 A293272 * A242028 A254002 A095729

Adjacent sequences: A192283 A192284 A192285 * A192287 A192288 A192289

Keyword

nonn

Author

Paolo P. Lava, Jul 28 2011

Extensions

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

Status

approved