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 A332619 #13 Dec 05 2022 04:46:14
%S A332619 1,3,4,6,6,12,8,12,11,18,12,24,14,24,24,23,18,33,20,36,32,36,24,48,27,
%T A332619 42,32,48,30,72,32,45,48,54,48,66,38,60,56,72,42,96,44,72,66,72,48,92,
%U A332619 51,81,72,84,54,96,72,96,80,90,60,144,62,96,88,88,84,144,68,108,96,144
%N A332619 a(n) = Sum_{d|n} lcm(d, n/d) / d.
%H A332619 Antti Karttunen, <a href="/A332619/b332619.txt">Table of n, a(n) for n = 1..20000</a>
%H A332619 <a href="/index/Ga#gcd">Index entries for sequences related to gcd's</a>.
%H A332619 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.
%F A332619 a(n) = Sum_{d|n} d / gcd(d, n/d).
%F A332619 From _Amiram Eldar_, Dec 05 2022: (Start)
%F A332619 Multiplicative with a(p^e) = (p^(e+2)-1)/(p^2-1) + e/2 if e is even, and (p^(e+2)-p)/(p^2-1) + (e + 1)/2 if e is odd.
%F A332619 Sum_{k=1..n} a(k) ~ c * n^2, where c = 7*zeta(6)/(8*zeta(5)) = 0.740543... . (End)
%p A332619 a:= n-> add(d/igcd(d, n/d), d=numtheory[divisors](n)):
%p A332619 seq(a(n), n=1..80); # _Alois P. Heinz_, Feb 17 2020
%t A332619 Table[Sum[LCM[d, n/d]/d, {d, Divisors[n]}], {n, 1, 70}]
%t A332619 f[p_, e_] := If[EvenQ[e], (p^(e + 2) - 1)/(p^2 - 1) + e/2, (p^(e + 2) - p)/(p^2 - 1) + (e + 1)/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Dec 05 2022 *)
%o A332619 (PARI) A332619(n) = sumdiv(n,d,lcm(d,n/d)/d); \\ _Antti Karttunen_, Nov 12 2021
%Y A332619 Cf. A055155, A057660, A057661, A057670, A332618.
%Y A332619 Cf. A013663, A013664.
%K A332619 nonn,mult
%O A332619 1,2
%A A332619 _Ilya Gutkovskiy_, Feb 17 2020