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 A305186 #33 Mar 04 2025 18:07:50
%S A305186 1,20160,24261120,1321205760,116064000000,489104179200,27811094169600,
%T A305186 86586540687360,1044361663787520,2339850240000000,41393302251840000,
%U A305186 32053931488051200,610296923230525440,560671658459136000,2815842631680000000,5674535530486824960
%N A305186 Number of invertible 4 X 4 matrices mod n.
%C A305186 Order of the group GL(4,Z_n).
%C A305186 Order of the automorphism group of the group (C_n)^4, where C_n is the cyclic group of order n.
%C A305186 For n > 2, a(n) is divisible by 23040.
%H A305186 Jianing Song, <a href="/A305186/b305186.txt">Table of n, a(n) for n = 1..10000</a>
%H A305186 C. J. Hillar and D. L. Rhea, <a href="http://arxiv.org/abs/math/0605185">Automorphisms of finite abelian groups</a>, arXiv:math/0605185 [math.GR], 2006.
%H A305186 C. J. Hillar and D. L. Rhea, <a href="http://www.jstor.org/stable/27642365">Automorphisms of finite abelian groups</a>, Amer. Math. Monthly 114 (2007), no 10, 917-923.
%H A305186 J. Overbey, W. Traves and J. Wojdylo, <a href="http://jeff.over.bz/papers/undergrad/on-the-keyspace-of-the-hill-cipher.pdf">On the Keyspace of the Hill Cipher</a>, Cryptologia, Vol. 29, Iss. 1, 2005.
%F A305186 Multiplicative with a(p^e) = (p - 1)*(p^2 - 1)*(p^3 - 1)*(p^4 - 1)*p^(16*e-10).
%F A305186 a(n) = n^16*Product_{primes p dividing n} (1 - 1/p^4)*(1 - 1/p^3)*(1 - 1/p^2)*(1 - 1/p).
%F A305186 a(n) = phi(n)*A011786(n) = A000010(n)*A011786(n).
%F A305186 Sum_{k=1..n} a(k) ~ c * n^17, where c = (1/17) * Product_{p prime} ((p^11 - p^9 - p^8 + 2*p^5 - p^2 - p + 1)/p^11) = 0.02958150406... . - _Amiram Eldar_, Oct 23 2022
%t A305186 {1}~Join~Array[#^16*Product[(1 - 1/p^4) (1 - 1/p^3) (1 - 1/p^2) (1 - 1/p), {p, FactorInteger[#][[All, 1]]}] &, 12, 2] (* _Michael De Vlieger_, May 27 2018 *)
%o A305186 (PARI) a(n)=my(f=factor(n)[, 1]); n^16*prod(i=1, #f, (1-1/f[i]^4)*(1-1/f[i]^3)*(1-1/f[i]^2)*(1-1/f[i]))
%o A305186 (Python)
%o A305186 from math import prod
%o A305186 from sympy import factorint
%o A305186 def A305186(n): return prod(p**((e<<3)-5<<1)*(p*(p*(p**3*(p**3*(p*(p-1)-1)+2)-1)-1)+1) for p,e in factorint(n).items()) # _Chai Wah Wu_, Mar 04 2025
%Y A305186 Row n=4 of A316622.
%Y A305186 Cf. A000252 (GL(2,Z_n)), A064767 (GL(3,Z_n)).
%Y A305186 Cf. A000056 (SL(2,Z_n)), A011785 (SL(3,Z_n)), A011786 (SL(4,Z_n)).
%Y A305186 Cf. A000010.
%K A305186 nonn,easy,mult
%O A305186 1,2
%A A305186 _Jianing Song_, May 27 2018