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

%I A379223 #15 Dec 22 2024 13:05:50
%S A379223 1,13,31,57,121,133,183,403,307,381,741,553,781,1093,871,993,1729,
%T A379223 1767,1407,2379,1723,1893,3751,2257,2801,3991,2863,4123,4953,3541,
%U A379223 3783,6897,5673,4557,7189,5113,5403,10153,7581,6321,9841,6973,9517,11323,8011,10431,12909,11811,9507,16093,10303,10713,22971,11557
%N A379223 Sum of the divisors of the n-th odd square: a(n) = sigma((2*n-1)^2).
%C A379223 Sequence contains duplicates. For example, a(314) = a(375) = 658749 and a(1007) = a(1279) = 6540807.
%H A379223 Antti Karttunen, <a href="/A379223/b379223.txt">Table of n, a(n) for n = 1..20000</a>
%F A379223 a(n) = A000203(A016754(n-1)).
%t A379223 Table[DivisorSigma[1,(2n-1)^2],{n,54}] (* _James C. McMahon_, Dec 22 2024 *)
%o A379223 (PARI) A379223(n) = sigma((2*n-1)^2);
%o A379223 (Python)
%o A379223 from math import prod
%o A379223 from sympy import factorint
%o A379223 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
%Y A379223 Cf. A000203, A016754, A065768 (same sequence sorted into ascending order, with duplicates removed), A379224 [= A065621(a(n))].
%Y A379223 First row and column of array A379220, first row of array A379221.
%K A379223 nonn
%O A379223 1,2
%A A379223 _Antti Karttunen_, Dec 21 2024