A354451 Number of middle divisors of 2*n-1.

1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2

Offset: 1

Author

Omar E. Pol, May 30 2022

Keywords

• nonn

Comments

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

a(n) is also the width of the terrace at the level 2*n-1 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-1). For more information about the subparts see A279387.

Crossrefs

Bisection of A067742.

Cf. A005408, A099774, A237048, A237270, A237271, A237593, A245092, A249351, A279387, A319529, A354452.

Programs

Mathematica

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

Formula

a(n) = A067742(2n-1).

a(n) = A067742(A005408(n-1)).