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

1,5

Comments

a(n) has a symmetric representation.

Links

Table of n, a(n) for n=1..78.

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Bisection of A048050.

Partial sums give A346869.

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

Sequence in context: A218538 A243163 A209490 * A326397 A140577 A068606

Adjacent sequences: A346876 A346877 A346878 * A346880 A346881 A346882

Keyword

nonn,easy

Author

Omar E. Pol, Aug 18 2021

Status

approved