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A354451
Number of middle divisors of 2*n-1.
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
1,8
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.
FORMULA
a(n) = A067742(2n-1).
a(n) = A067742(A005408(n-1)).
MATHEMATICA
a[n_] := DivisorSum[2*n - 1, 1 &, n <= #^2 < 4*n - 2 &]; Array[a, 100] (* Amiram Eldar, Jun 01 2022 *)
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 30 2022
STATUS
approved