A354452 Number of middle divisors of 2*n.

1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 0, 2, 0, 1, 2, 0, 2, 3, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2, 0, 3, 0, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, 1, 2, 1, 0, 2, 0, 2, 2

Offset

1,3

Comments

a(n) is the number of middle divisors of the n-th even number.

a(n) is also the width of the terrace at the level 2*n starting from the top in the main diagonal of the stepped pyramid described in A245092.

a(n) is also the number of central subparts in the symmetric representation of sigma(2n). For more information about the subparts see A279387.

Links

Table of n, a(n) for n=1..105.

Formula

a(n) = A067742(2n).

a(n) = A067742(A005843(n)).

Mathematica

a[n_] := DivisorSum[2*n, 1 &, n <= #^2 < 4*n &]; Array[a, 100] (* Amiram Eldar, Jun 01 2022 *)

Crossrefs

Bisection of A067742.

Cf. A005843, A099777, A237048, A237270, A237271, A237593, A245092, A249351, A279387, A319796, A354451.

Sequence in context: A143614 A071412 A080884 * A362450 A298731 A321102

Adjacent sequences: A354449 A354450 A354451 * A354453 A354454 A354455

Keyword

nonn

Author

Omar E. Pol, May 30 2022

Status

approved