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 A337532 a(n) = Sum_{d1|n, d2|n, d1<=d2} [(d1 mod 2) = (d2 mod 2)], where [ ] is the Iverson bracket. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000217(A000005(A000265(n)) + A000217(A000005(A000265(n))*A007814(n)). - Robert Israel, Nov 01 2020 MAPLE 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: map(f, [\$1..100]); # Robert Israel, Nov 01 2020 MATHEMATICA 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}] CROSSREFS Cf. A000005, A000217, A000265, A007814. Sequence in context: A317588 A080383 A086369 * A092089 A117659 A079065 Adjacent sequences:  A337529 A337530 A337531 * A337533 A337534 A337535 KEYWORD nonn,look AUTHOR Wesley Ivan Hurt, Aug 30 2020 STATUS approved

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Last modified June 12 14:10 EDT 2021. Contains 344952 sequences. (Running on oeis4.)