

A337532


a(n) = Sum_{d1n, d2n, 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
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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



