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 A334579 #15 Sep 08 2022 08:46:25
%S A334579 1,2,3,3,3,8,3,4,4,6,3,11,3,8,9,5,3,12,3,13,9,8,3,16,4,6,8,11,3,24,3,
%T A334579 8,9,6,9,16,3,8,9,16,3,26,3,15,16,8,3,19,6,10,9,9,3,24,9,20,9,6,3,45,
%U A334579 3,8,12,9,9,26,3,13,9,24,3,24,3,6,12,11,9,24,3
%N A334579 a(n) = Sum_{d|n} gcd(tau(d), sigma(d)).
%C A334579 Inverse Möbius transform of A009205. - _Antti Karttunen_, May 19 2020
%H A334579 Antti Karttunen, <a href="/A334579/b334579.txt">Table of n, a(n) for n = 1..16384</a>
%H A334579 Antti Karttunen, <a href="/A334579/a334579.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A334579 a(p) = 3 for p = odd primes (A065091).
%e A334579 a(6) = gcd(tau(1), sigma(1)) + gcd(tau(2), sigma(2)) + gcd(tau(3), sigma(3)) + gcd(tau(6), sigma(6)) = gcd(1, 1) + gcd(2, 3) + gcd(2, 4) + gcd(4, 12) = 1 + 1 + 2 + 4 = 8.
%t A334579 a[n_] := DivisorSum[n, GCD[DivisorSigma[0, #], DivisorSigma[1, #]] &]; Array[a, 100] (* _Amiram Eldar_, May 07 2020 *)
%o A334579 (Magma) [&+[GCD(#Divisors(d), &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o A334579 (PARI) a(n) = sumdiv(n, d, gcd(numdiv(d), sigma(d))); \\ _Michel Marcus_, May 07 2020
%Y A334579 Cf. A322979 (Sum_{d|n} gcd(d, tau(d))), A334490 (Sum_{d|n} gcd(d, sigma(d))).
%Y A334579 Cf. A000005 (tau(n)), A000203 (sigma(n)), A009205 (gcd(tau(n), sigma(n))).
%Y A334579 Cf. A334729 (with product, instead of sum).
%K A334579 nonn
%O A334579 1,2
%A A334579 _Jaroslav Krizek_, May 06 2020