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%I #30 Dec 22 2024 09:19:27
%S 1,13,31,57,121,133,183,307,381,403,553,741,781,871,993,1093,1407,
%T 1723,1729,1767,1893,2257,2379,2801,2863,3541,3751,3783,3991,4123,
%U 4557,4953,5113,5403,5673,6321,6897,6973,7189,7581,8011,9507,9517,9841,10153
%N Numbers that are sums of divisors of the odd squares; Intersection of A065764 and A065766, written in ascending order and duplicates removed.
%C 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
%C Equally, the sum of divisors (A000203) as only odd divisors are present in odd squares. - _Antti Karttunen_, Dec 22 2024
%H Amiram Eldar, <a href="/A065768/b065768.txt">Table of n, a(n) for n = 1..10000</a>
%t 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 *)
%Y Cf. A000203, A000593, A016754, A065764, A065766, A274790.
%Y Sequence A379223 sorted into ascending order, with duplicates removed.
%K nonn
%O 1,2
%A _Labos Elemer_, Nov 19 2001
%E Old definition clarified and _Timothy L. Tiffin_'s comment adopted as a new primary definition - _Antti Karttunen_, Dec 22 2024