A065768 Numbers that are sums of divisors of the odd squares; Intersection of A065764 and A065766, written in ascending order and duplicates removed.

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

Offset

1,2

Comments

Terms are the sum of the odd divisors (A000593) of the odd squares (A016754), written in ascending order. Subsequence of the odd terms of A274790. - Timothy L. Tiffin, Feb 12 2022

Equally, the sum of divisors (A000203) as only odd divisors are present in odd squares. - Antti Karttunen, Dec 22 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

f1[p_, e_] := (p^(2*e + 1) - 1)/(p - 1); s1[1] = 1; s1[n_] := Times @@ f1 @@@ FactorInteger[n]; f2[p_, e_] := (p^(2*e + 1) - 1)/(p - 1); f2[2, e_] := (4^(e + 1) - 1)/3; s2[1] = 1; s2[n_] := Times @@ f2 @@@ FactorInteger[n]; seq[max_] := Intersection[Select[Array[s1, max], # < max^2 &], Select[Array[s2, max], # < max^2 &]]; seq[101] (* Amiram Eldar, Aug 24 2024 *)

Crossrefs

Cf. A000203, A000593, A016754, A065764, A065766, A274790.

Sequence A379223 sorted into ascending order, with duplicates removed.

Sequence in context: A063305 A301622 A166143 * A379223 A155820 A242231

Adjacent sequences: A065765 A065766 A065767 * A065769 A065770 A065771

Keyword

nonn

Author

Labos Elemer, Nov 19 2001

Extensions

Old definition clarified and Timothy L. Tiffin's comment adopted as a new primary definition - Antti Karttunen, Dec 22 2024

Status

approved