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 A349130 #19 Nov 14 2021 17:44:16
%S A349130 1,3,5,7,9,15,13,15,19,27,21,35,25,39,45,31,33,57,37,63,65,63,45,75,
%T A349130 61,75,65,91,57,135,61,63,105,99,117,133,73,111,125,135,81,195,85,147,
%U A349130 171,135,93,155,127,183,165,175,105,195,189,195,185,171,117,315,121,183,247,127,225,315,133,231,225,351,141
%N A349130 a(n) = Sum_{d|n} d * A003958(n/d), where A003958 is fully multiplicative with a(p) = (p-1).
%C A349130 Dirichlet convolution of A003958 with the identity function, A000027.
%C A349130 Dirichlet convolution of sigma (A000203) with A003966.
%H A349130 Antti Karttunen, <a href="/A349130/b349130.txt">Table of n, a(n) for n = 1..20000</a>
%F A349130 a(n) = Sum_{d|n} d * A003958(n/d).
%F A349130 a(n) = Sum_{d|n} A349131(d).
%F A349130 a(n) = Sum_{d|n} A000203(d) * A003966(n/d).
%F A349130 a(n) = A038040(n) - A348980(n).
%F A349130 For all n >= 1, a(n) <= A349129(n) <= A349170(n).
%F A349130 Multiplicative with a(p^e) = p^(e+1) - (p-1)^(e+1). - _Amiram Eldar_, Nov 09 2021
%t A349130 f[p_, e_] := p^(e + 1) - (p - 1)^(e + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 09 2021 *)
%o A349130 (PARI)
%o A349130 A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
%o A349130 A349130(n) = sumdiv(n,d,d*A003958(n/d));
%Y A349130 Cf. A000203, A003958, A003966, A038040, A348980, A349129, A349131 (Möbius transform), A349132, A349133, A349170.
%K A349130 nonn,mult
%O A349130 1,2
%A A349130 _Antti Karttunen_, Nov 09 2021