A346879 Sum of the divisors, except the smallest and the largest, of the n-th odd number.

0, 0, 0, 0, 3, 0, 0, 8, 0, 0, 10, 0, 5, 12, 0, 0, 14, 12, 0, 16, 0, 0, 32, 0, 7, 20, 0, 16, 22, 0, 0, 40, 18, 0, 26, 0, 0, 48, 18, 0, 39, 0, 22, 32, 0, 20, 34, 24, 0, 56, 0, 0, 86, 0, 0, 40, 0, 28, 64, 24, 11, 44, 30, 0, 46, 0, 26, 104, 0, 0, 50, 24, 34, 80, 0, 0, 80, 36

Offset: 1

Author

Omar E. Pol, Aug 18 2021

Keywords

• nonn
• easy

Comments

a(n) has a symmetric representation.

Examples

			For n = 5 the 5th odd number is 9 and the divisors of 9 are [1, 3, 9] and the sum of the divisors of 9 except the smaller and the largest is 3, so a(5) = 3.
For n = 6 the 6th odd number is 11 and the divisors of 11 are [1, 11] and the sum of the divisors of 11 except the smaller and the largest is 0, so a(6) = 0.
		

Crossrefs

Bisection of A048050.

Partial sums give A346869.

Cf. A000203, A005408, A008438, A237593, A245092, A244049, A326123, A346880.

Programs

Mathematica

a[1] = 0; a[n_] := DivisorSigma[1, 2*n - 1] - 2*n; Array[a, 100] (* Amiram Eldar, Aug 19 2021 *)

Python

from sympy import divisors
def a(n): return sum(divisors(2*n-1)[1:-1])
print([a(n) for n in range(1, 79)]) # Michael S. Branicky, Aug 19 2021

Formula

a(n) = A048050(2*n-1).