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

Author

Labos Elemer, Nov 19 2001

Keywords

• nonn

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

Crossrefs

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

Sequence A379223 sorted into ascending order, with duplicates removed.

Programs

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 *)

Extensions

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