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 A349225 #15 Nov 08 2022 08:06:57
%S A349225 1,6,8,19,28,30,80,93,119,126,136,156,186,192,205,312,351,384,448,483,
%T A349225 567,774,820,896,945,1081,1100,1187,1240,1375,1464,2268,2628,2720,
%U A349225 2898,3197,3744,3840,4544,4992,5079,6200,6567,7296,7832,9184,12288,12636,16578
%N A349225 Numbers k such that k | A002619(k).
%C A349225 Chao (1982) proved that k | Sum_{d|k} phi(d)^2*d^(k/d-1)*(k/d-1)! for all k. The quotients are A002619(k). This sequence consists of numbers k such that this sum is divisible by k^2.
%C A349225 There are terms k such that k^2 | A002619(k): 1, 8, 1081, ...
%D A349225 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 3, p. 192.
%H A349225 Amiram Eldar, <a href="/A349225/b349225.txt">Table of n, a(n) for n = 1..200</a>
%H A349225 Chong-Yun Chao, <a href="https://doi.org/10.1016/0022-314X(82)90085-3">Generalizations of theorems of Wilson, Fermat and Euler</a>, Journal of Number Theory, Vol. 15, No. 1 (1982), pp. 95-114.
%e A349225 6 is a term since A002619(6) = 24 is divisible by 6.
%t A349225 f[n_] := DivisorSum[n, EulerPhi[#]^2 * #^(n/#) * (n/#)! &]/n^2; Select[Range[1000], Divisible[f[#], #] &]
%o A349225 (Python)
%o A349225 from itertools import count, islice
%o A349225 from sympy import divisors, totient, factorial
%o A349225 def A349225_gen(startvalue=1): # generator of terms >= startvalue
%o A349225 return filter(lambda n:not sum(totient(m:=n//d)**2*factorial(d)*m**d for d in divisors(n,generator=True)) % n**3, count(max(startvalue,1)))
%o A349225 A349225_list = list(islice(A349225_gen(),10)) # _Chai Wah Wu_, Nov 07 2022
%Y A349225 Cf. A000010 (phi), A002619.
%K A349225 nonn
%O A349225 1,2
%A A349225 _Amiram Eldar_, Nov 11 2021