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A346879 Sum of the divisors, except the smallest and the largest, of the n-th odd number. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 21 18:55 EDT 2022. Contains 353926 sequences. (Running on oeis4.)