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
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
KEYWORD
nonn,look
AUTHOR
Wesley Ivan Hurt, Aug 30 2020
STATUS
approved