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A211225
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Number of ways to represent sigma(n) as sigma(x) + sigma(y) where x+y = n.
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8
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0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2
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OFFSET
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1,32
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COMMENTS
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From an idea of Charles R Greathouse IV.
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LINKS
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EXAMPLE
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a(3)=1 because sigma(3)=sigma(1)+sigma(2)=4;
a(32)=2 because sigma(32)=sigma(4)+sigma(28)=sigma(14)+sigma(18)=63;
a(117)=3 because sigma(117)=sigma(41)+sigma(76)=sigma(52)+sigma(65)=sigma(56)+sigma(61)=182; etc.
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MAPLE
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with(numtheory);
local b, i, n;
for n from 1 to q do
b:=0;
for i from 1 to trunc(n/2) do
if sigma(i)+sigma(n-i)=sigma(n) then b:=b+1; fi;
od;
print(b)
od; end:
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MATHEMATICA
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a[n_] := With[{s = DivisorSigma[1, n]}, Sum[Boole[s == DivisorSigma[1, x] + DivisorSigma[1, n-x]], {x, 1, Quotient[n, 2]}]];
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PROG
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(Haskell)
a211225 n = length $ filter (== a000203 n) $ zipWith (+) us' vs where
(us, vs@(v:_)) = splitAt (fromInteger $ (n - 1) `div` 2) a000203_list
us' = if even n then v : reverse us else reverse us
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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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