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A192286
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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.
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0
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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
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..37.
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FORMULA
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Like A020487 but using anti-divisors.
4, 9, 36, 576, 1296, etc. are antiharmonic both with divisors and anti-divisors.
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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Cf. A020487, A066272.
Sequence in context: A350741 A191699 A293272 * A242028 A254002 A095729
Adjacent sequences: A192283 A192284 A192285 * A192287 A192288 A192289
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KEYWORD
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nonn
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AUTHOR
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Paolo P. Lava, Jul 28 2011
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EXTENSIONS
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a(22)-a(37) from Donovan Johnson, Sep 22 2011
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STATUS
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approved
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