A337532 a(n) = Sum_{d1|n, d2|n, d1<=d2} [(d1 mod 2) = (d2 mod 2)], where [ ] is the Iverson bracket.

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

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