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A335841 Number of distinct rectangles that can be made with one even and one odd side length that are divisors of 2n. 0
1, 2, 4, 3, 4, 8, 4, 4, 9, 8, 4, 12, 4, 8, 16, 5, 4, 18, 4, 12, 16, 8, 4, 16, 9, 8, 16, 12, 4, 32, 4, 6, 16, 8, 16, 27, 4, 8, 16, 16, 4, 32, 4, 12, 36, 8, 4, 20, 9, 18, 16, 12, 4, 32, 16, 16, 16, 8, 4, 48, 4, 8, 36, 7, 16, 32, 4, 12, 16, 32, 4, 36, 4, 8, 36, 12, 16, 32, 4, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..80.

FORMULA

a(n) = Sum_{d1|(2*n), d2|(2*n), d1<d2} (1 - [d1 mod 2 = d2 mod 2]), where [ ] is the Iverson bracket.

EXAMPLE

a(6) = 8; The divisors of 2*6 = 12 are {1,2,3,4,6,12}. There are 8 distinct rectangles with one odd and one even side length using these divisors. They are 1 X 2, 1 X 4, 1 X 6, 1 X 12, 2 X 3, 3 X 4, 3 X 6, and 3 X 12.

MATHEMATICA

Table[Sum[Sum[KroneckerDelta[Mod[i + 1, 2], Mod[k, 2]]*(1 - Ceiling[2n/k] + Floor[2n/k]) (1 - Ceiling[2n/i] + Floor[2n/i]), {i, k-1}], {k, 2n}], {n, 100}]

CROSSREFS

Cf. A337532.

Sequence in context: A087794 A050514 A229047 * A133702 A328486 A332224

Adjacent sequences:  A335838 A335839 A335840 * A335842 A335843 A335844

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 13 2020

STATUS

approved

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Last modified May 15 08:59 EDT 2021. Contains 343909 sequences. (Running on oeis4.)