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 A334490 #22 Sep 08 2022 08:46:25
%S A334490 1,2,2,3,2,9,2,4,3,5,2,14,2,5,6,5,2,13,2,8,4,5,2,27,3,5,4,34,2,21,2,6,
%T A334490 6,5,4,19,2,5,4,19,2,19,2,10,10,5,2,32,3,7,6,8,2,20,4,43,4,5,2,40,2,5,
%U A334490 6,7,4,21,2,8,6,11,2,35,2,5,8,10,4,19,2,22
%N A334490 a(n) = Sum_{d|n} gcd(d, sigma(d)).
%H A334490 Antti Karttunen, <a href="/A334490/b334490.txt">Table of n, a(n) for n = 1..16384</a>
%H A334490 Antti Karttunen, <a href="/A334490/a334490.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A334490 a(p) = 2 for p = primes (A000040).
%F A334490 a(n) = Sum_{d|n} A009194(d). - _Antti Karttunen_, May 09 2020
%e A334490 a(6) = gcd(1, sigma(1)) + gcd(2, sigma(2)) + gcd(3, sigma(3)) + gcd(6, sigma(6)) = gcd(1, 1) + gcd(2, 3) + gcd(3, 4) + gcd(6, 12) = 1 + 1 + 1 + 6 = 9.
%t A334490 a[n_] := DivisorSum[n, GCD[#, DivisorSigma[1, #]] &]; Array[a, 80] (* _Amiram Eldar_, May 03 2020 *)
%o A334490 (Magma) [&+[GCD(d, &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o A334490 (PARI) a(n) = sumdiv(n, d, gcd(d, sigma(d))); \\ _Michel Marcus_, May 03 2020
%Y A334490 Cf. A322979 (Sum_{d|n} gcd(d, tau(d))), A000203 (Sum_{d|n} gcd(d, pod(d)) = sigma(n)).
%Y A334490 Cf. A000040, A007955 (pod(n)), A334491 (for product instead of sum).
%Y A334490 Inverse Möbius transform of A009194.
%K A334490 nonn
%O A334490 1,2
%A A334490 _Jaroslav Krizek_, May 03 2020