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 A062363 #31 Jun 16 2025 08:44:17
%S A062363 0,1,3,7,27,121,729,5041,40347,362887,3628923,39916801,479002353,
%T A062363 6227020801,87178296243,1307674368127,20922789928347,355687428096001,
%U A062363 6402373706091609,121645100408832001,2432902008180268947,51090942171709445047,1124000727777647596803
%N A062363 a(n) = Sum_{d|n} d!.
%H A062363 Harry J. Smith, <a href="/A062363/b062363.txt">Table of n, a(n) for n = 0..100</a>
%F A062363 G.f.: Sum_{m>0} m!*x^m/(1-x^m). - _Vladeta Jovovic_, Aug 06 2004
%F A062363 Inverse Moebius transform of factorials (A000142). - _Jonathan Vos Post_, Mar 19 2006
%F A062363 a(n) ~ n!. - _Vaclav Kotesovec_, Mar 14 2015
%F A062363 L.g.f.: -log(Product_{k>=1} (1 - x^k)^((k-1)!)) = Sum_{n>=1} a(n)*x^n/n. - _Ilya Gutkovskiy_, May 23 2018
%e A062363 The divisors of 3 are 1 and 3 so 1! + 3! = 7. The divisors of 4 are 1, 2 and 4 so 1! + 2! + 4! = 27.
%t A062363 nmax=20; CoefficientList[Series[Sum[m!*x^m/(1-x^m),{m,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Mar 14 2015 *)
%t A062363 Join[{0},Table[Total[Divisors[n]!],{n,20}]] (* _Harvey P. Dale_, Aug 15 2024 *)
%o A062363 (PARI) a(n)=if(n<1, 0, sumdiv(n, d, d!));
%Y A062363 Cf. A000142, A179327.
%K A062363 easy,nonn
%O A062363 0,3
%A A062363 _Jason Earls_, Jul 07 2001