This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379482 #17 Dec 27 2024 18:18:24
%S A379482 1,13,31,121,57,403,133,1093,781,741,183,3751,307,1729,1767,9841,381,
%T A379482 10153,553,6897,4123,2379,871,33883,2801,3991,19531,16093,993,22971,
%U A379482 1407,88573,5673,4953,7581,94501,1723,7189,9517,62301,1893,53599,2257,22143,44517,11323,2863,305071,16105,36413,11811,37147,3541
%N A379482 a(n) = sigma(A003961(n^2)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.
%H A379482 Antti Karttunen, <a href="/A379482/b379482.txt">Table of n, a(n) for n = 1..20000</a>
%H A379482 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A379482 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379482 Multiplicative with a(p^e) = (q^(2e+1) - 1)/(q-1), where q = nextprime(p) = A151800(p).
%F A379482 a(n) = A000203(A379481(n)) = A003973(A000290(n)).
%F A379482 a(n) = A379223(A048673(n)).
%F A379482 a(n) = 2*A379481(n) - A378231(n).
%t A379482 {1}~Join~Array[DivisorSigma[1, #] &[Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]] ]^2] &, 52, 2] (* _Michael De Vlieger_, Dec 27 2024 *)
%o A379482 (PARI) A379482(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1); f[i, 2] *= 2); sigma(factorback(f)); };
%Y A379482 Cf. A000290, A003973, A048673, A151800, A378231, A379223, A379481, A379483, A379484 [= A038500(a(n))].
%Y A379482 Cf. also A337336, A337337.
%K A379482 nonn,mult
%O A379482 1,2
%A A379482 _Antti Karttunen_, Dec 27 2024