A379223 Sum of the divisors of the n-th odd square: a(n) = sigma((2*n-1)^2).

1, 13, 31, 57, 121, 133, 183, 403, 307, 381, 741, 553, 781, 1093, 871, 993, 1729, 1767, 1407, 2379, 1723, 1893, 3751, 2257, 2801, 3991, 2863, 4123, 4953, 3541, 3783, 6897, 5673, 4557, 7189, 5113, 5403, 10153, 7581, 6321, 9841, 6973, 9517, 11323, 8011, 10431, 12909, 11811, 9507, 16093, 10303, 10713, 22971, 11557

Offset

1,2

Comments

Sequence contains duplicates. For example, a(314) = a(375) = 658749 and a(1007) = a(1279) = 6540807.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = A000203(A016754(n-1)).

Mathematica

Table[DivisorSigma[1, (2n-1)^2], {n, 54}] (* James C. McMahon, Dec 22 2024 *)

Prog

(PARI) A379223(n) = sigma((2*n-1)^2);
(Python)
from math import prod
from sympy import factorint
def A379223(n): return prod((p**((e<<1)|1)-1)//(p-1) for p, e in factorint((n<<1)-1).items()) # Chai Wah Wu, Dec 21 2024

Crossrefs

Cf. A000203, A016754, A065768 (same sequence sorted into ascending order, with duplicates removed), A379224 [= A065621(a(n))].

First row and column of array A379220, first row of array A379221.

Sequence in context: A301622 A166143 A065768 * A155820 A242231 A330855

Adjacent sequences: A379220 A379221 A379222 * A379224 A379225 A379226

Keyword

nonn,new

Author

Antti Karttunen, Dec 21 2024

Status

approved