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 A349129 #12 Nov 14 2021 17:44:07
%S A349129 1,4,6,13,10,24,14,40,28,40,22,78,26,56,60,121,34,112,38,130,84,88,46,
%T A349129 240,76,104,120,182,58,240,62,364,132,136,140,364,74,152,156,400,82,
%U A349129 336,86,286,280,184,94,726,148,304,204,338,106,480,220,560,228,232,118,780,122,248,392,1093,260,528,134,442,276
%N A349129 a(n) = Sum_{d|n} A003958(d) * A003959(n/d), where A003958 is fully multiplicative with a(p) = (p-1), and A003959 is fully multiplicative with a(p) = (p+1).
%C A349129 Dirichlet convolution of A003958 with A003959.
%H A349129 Antti Karttunen, <a href="/A349129/b349129.txt">Table of n, a(n) for n = 1..20000</a>
%F A349129 Multiplicative with a(p^e) = ((p+1)^(e+1) - (p-1)^(e+1))/2. - _Amiram Eldar_, Nov 09 2021
%F A349129 For all n >= 1, A349130(n) <= a(n) <= A349170(n).
%t A349129 f[p_, e_] := ((p + 1)^(e + 1) - (p - 1)^(e + 1))/2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 09 2021 *)
%o A349129 (PARI)
%o A349129 A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
%o A349129 A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A349129 A349129(n) = sumdiv(n,d,A003958(d)*A003959(n/d));
%Y A349129 Cf. A003958, A003959, A168066, A349139.
%Y A349129 Cf. also A349130, A349131, A349132, A349133 and A349170, A349171, A349172, A349173.
%K A349129 nonn,mult
%O A349129 1,2
%A A349129 _Antti Karttunen_, Nov 09 2021