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A337532
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a(n) = Sum_{d1|n, d2|n, d1<=d2} [(d1 mod 2) = (d2 mod 2)], where [ ] is the Iverson bracket.
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2
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1, 2, 3, 4, 3, 6, 3, 7, 6, 6, 3, 13, 3, 6, 10, 11, 3, 12, 3, 13, 10, 6, 3, 24, 6, 6, 10, 13, 3, 20, 3, 16, 10, 6, 10, 27, 3, 6, 10, 24, 3, 20, 3, 13, 21, 6, 3, 39, 6, 12, 10, 13, 3, 20, 10, 24, 10, 6, 3, 46, 3, 6, 21, 22, 10, 20, 3, 13, 10, 20, 3, 51, 3, 6, 21, 13, 10, 20, 3, 39
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OFFSET
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1,2
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COMMENTS
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Number of distinct rectangles that can be made whose side lengths are divisors of n and whose length and width are either both odd or both even.
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LINKS
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FORMULA
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MAPLE
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f:= proc(n) local t, m, n1, n2; t:= padic:-ordp(n, 2);
m:= n/2^t;
n1:= numtheory:-tau(m);
n2:= n1*t;
(n1*(n1+1)+n2*(n2+1))/2;
end proc:
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MATHEMATICA
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Table[Sum[Sum[KroneckerDelta[Mod[i, 2], Mod[k, 2]]*(1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 100}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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