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

%I #18 Jul 26 2022 14:04:42

%S 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,

%T 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,

%U 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

%N Number of middle divisors of 2*n-1.

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

%C 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.

%C 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.

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

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

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

%Y Bisection of A067742.

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

%K nonn

%O 1,8

%A _Omar E. Pol_, May 30 2022