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 A055210 #37 Nov 13 2022 08:39:23
%S A055210 1,1,1,3,1,1,1,3,7,1,1,3,1,1,1,11,1,7,1,3,1,1,1,3,21,1,7,3,1,1,1,11,1,
%T A055210 1,1,21,1,1,1,3,1,1,1,3,7,1,1,11,43,21,1,3,1,7,1,3,1,1,1,3,1,1,7,43,1,
%U A055210 1,1,3,1,1,1,21,1,1,21,3,1,1,1,11,61,1,1,3,1,1,1,3,1,7,1,3,1,1,1,11,1
%N A055210 Sum of totients of square divisors of n.
%H A055210 Antti Karttunen, <a href="/A055210/b055210.txt">Table of n, a(n) for n = 1..16384</a>
%F A055210 a(n) = Sum_{d is square and divides n} phi(d).
%F A055210 Multiplicative with a(p^e) = (p^(e+1)+1)/(p+1) for even e and a(p^e) = (p^e+1)/(p+1) for odd e. - _Vladeta Jovovic_, Dec 01 2001
%F A055210 a(n) = Sum_{d|n} A010052(d)*A000010(d). - _Antti Karttunen_, Nov 18 2017
%F A055210 Conjecture: a(n) = sigma_2(n/core(n))/sigma_1(n/core(n)) = A001157(A008833(n))/A000203(A008833(n)) for all n > 0. - _Velin Yanev_, Oct 13 2019
%F A055210 G.f.: Sum_{k>=1} k * phi(k) * x^(k^2) / (1 - x^(k^2)). - _Ilya Gutkovskiy_, Aug 20 2021
%F A055210 Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = zeta(3/2)/(3*zeta(2)) = 0.529377... . - _Amiram Eldar_, Nov 13 2022
%e A055210 n = 400: its square divisors are {1, 4, 16, 25, 100, 400}, their totients are {1, 2, 8, 20, 40, 160} and the totient-sum over these divisors is, so a(400) = 231. This value arises at special squarefree multiples of 400 (400 times 2, 3, 5, 6, 7, 10, 11, 13, 15, 17, 19, 21, 22, 23 etc).
%e A055210 a(400) = a(2^4*5^2) = (2^5 + 1)/3*(5^3 + 1)/6 = 231.
%t A055210 Array[DivisorSum[#, EulerPhi, IntegerQ@ Sqrt@ # &] &, 97] (* _Michael De Vlieger_, Nov 18 2017 *)
%t A055210 f[p_, e_] := If[EvenQ[e], (p^(e + 1) + 1)/(p + 1), (p^e + 1)/(p + 1)]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Dec 09 2020 *)
%o A055210 (PARI) a(n) = sumdiv(n, d, eulerphi(d)*issquare(d)); \\ _Michel Marcus_, Dec 31 2013
%o A055210 (Magma) [&+[EulerPhi(d):d in Divisors(n)| IsSquare(d)]: n in [1..100]]; // _Marius A. Burtea_, Oct 14 2019
%Y A055210 Cf. A000010, A010052, A013661, A078434.
%K A055210 nonn,mult
%O A055210 1,4
%A A055210 _Labos Elemer_, Jun 19 2000