login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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