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A211217
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Maximum of sigma(x) * sigma(y), where x + y = n.
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4
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1, 3, 9, 12, 21, 28, 49, 48, 84, 72, 144, 96, 180, 156, 225, 195, 336, 234, 420, 364, 504, 360, 784, 432, 672, 672, 868, 576, 1092, 744, 1176, 936, 1209, 1008, 1680, 992, 1638, 1440, 1860, 1344, 2340, 1344, 2520, 1920, 2232, 1680, 3600, 1860, 3024, 2400
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OFFSET
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2,2
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LINKS
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EXAMPLE
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For n=83 the maximum product is reached when 35 and 48 (35+48=83) are considered: sigma(35)*sigma(48) = 48*124 = 5952.
For n=99 the maximum product is reached when 36 and 63 (36+63=99) are considered: sigma(36)*sigma(63) = 91*104 = 9464.
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MAPLE
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with(combstruct); with(numtheory);
local a, b, j, n, t;
for n from 2 to i do
t:=0;
for j from 0 to floor(n/2) do
a:=n-j; b:=sigma(j)*sigma(a); if b>t then t:=b; fi;
od;
print(t);
od; end:
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MATHEMATICA
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a[n_] := Max[Times @@ DivisorSigma[1, #]& /@ IntegerPartitions[n, {2}]]; Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Dec 26 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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