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A062363 a(n) = Sum_{d|n} d!. 8

%I

%S 0,1,3,7,27,121,729,5041,40347,362887,3628923,39916801,479002353,

%T 6227020801,87178296243,1307674368127,20922789928347,355687428096001,

%U 6402373706091609,121645100408832001,2432902008180268947

%N a(n) = Sum_{d|n} d!.

%H Harry J. Smith, <a href="/A062363/b062363.txt">Table of n, a(n) for n = 0..100</a>

%F G.f.: Sum_{m>0} m!*x^m/(1-x^m). - _Vladeta Jovovic_, Aug 06 2004

%F Inverse Moebius transform of factorials (A000142). - _Jonathan Vos Post_, Mar 19 2006

%F a(n) ~ n!. - _Vaclav Kotesovec_, Mar 14 2015

%F 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 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 nmax=20; CoefficientList[Series[Sum[m!*x^m/(1-x^m),{m,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Mar 14 2015 *)

%o (PARI) a(n)=if(n<1, 0, sumdiv(n, d, d!));

%Y Cf. A000142, A179327.

%K easy,nonn

%O 0,3

%A _Jason Earls_, Jul 07 2001

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)