

A192286


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


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS

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


FORMULA

Like A020487 but using antidivisors.
4, 9, 36, 576, 1296, etc. are antiharmonic both with divisors and antidivisors.


EXAMPLE

Antidivisors of 1212 are 5, 8, 24, 25, 97, 485, 808 and their sum is 1452. The sum of the squares of antidivisors 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 i1 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



