login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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