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 A057670 #42 Aug 27 2023 04:34:43
%S A057670 1,4,6,10,10,24,14,24,21,40,22,60,26,56,60,52,34,84,38,100,84,88,46,
%T A057670 144,55,104,72,140,58,240,62,112,132,136,140,210,74,152,156,240,82,
%U A057670 336,86,220,210,184,94,312,105,220,204,260,106,288,220,336,228,232,118,600
%N A057670 a(n) = Sum_{k|n} lcm(k, n/k).
%H A057670 G. C. Greubel, <a href="/A057670/b057670.txt">Table of n, a(n) for n = 1..10000</a>
%H A057670 László Tóth, <a href="https://arxiv.org/abs/1310.7053">Multiplicative arithmetic functions of several variables: a survey</a>, arXiv:1310.7053 [math.NT], 2013-2014.
%F A057670 Multiplicative with a(p) = 2*p, a(p^k) = (2*p^(k+1) - p^ceiling((k+1)/2) - p^floor((k+1)/2)) / (p-1). a(n) is odd iff n is an odd square. - _Henry Bottomley_, May 16 2005
%F A057670 Multiplicative with a(p^e) = Sum_{k=0..e} p^max(k, e-k), (cf. A107661). - _Mitch Harris_, May 18 2005
%F A057670 Dirichlet g.f.: (zeta(s-1))^2*zeta(2s-1)/zeta(2s-2). - _R. J. Mathar_, Feb 11 2011
%F A057670 Sum_{k=1..n} a(k) ~ 3*zeta(3)*n^2 / (2*Pi^2) * (2*log(n) - 24*zeta'(2)/Pi^2 - 1 + 4*gamma + 4*zeta'(3)/zeta(3)), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Feb 01 2019
%e A057670 a(8) = lcm(1,8) + lcm(2,4) + lcm(4,2) + lcm(8,1) = 8 + 4 + 4 + 8 = 24.
%t A057670 Table[DivisorSum[n, LCM[#, n/#] &], {n, 59}] (* _Michael De Vlieger_, Dec 11 2017 *)
%t A057670 f[p_, e_] := (2*p^(e + 1) - p^Ceiling[(e + 1)/2] - p^Floor[(e + 1)/2])/(p - 1); f[p_, 1] := 2*p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 60] (* _Amiram Eldar_, Aug 27 2023 *)
%o A057670 (PARI) a(n) = sumdiv(n, d, lcm(d, n/d)); \\ _Michel Marcus_, May 19 2014
%Y A057670 Cf. A001620, A055155, A107661.
%K A057670 nonn,mult,easy
%O A057670 1,2
%A A057670 _Leroy Quet_, Oct 18 2000