

A346879


Sum of the divisors, except the smallest and the largest, of the nth 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
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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*n1).


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*n1)[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



