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a(n) = Sum_{d divides n} (d!)^(n/d).
4

%I #16 Dec 20 2023 18:58:29

%S 1,3,7,29,121,765,5041,40913,363097,3643233,39916801,479535185,

%T 6227020801,87203692929,1307676103777,20924415922433,355687428096001,

%U 6402505760917569,121645100408832001,2432915176581403649,51090942299733783937,1124002321128529922049

%N a(n) = Sum_{d divides n} (d!)^(n/d).

%H Seiichi Manyama, <a href="/A217576/b217576.txt">Table of n, a(n) for n = 1..449</a>

%F G.f.: Sum_{n>=1} n!*x^n / (1 - n!*x^n). - _Paul D. Hanna_, Jan 17 2013

%t f[n_]=With[{d=Divisors[n]},Total[(d!)^(n/d)]]; Array[f,25] (* _Harvey P. Dale_, Dec 20 2023 *)

%o (PARI) a(n)=sumdiv(n,d, (d!)^(n/d) );

%Y Cf. A062363 ( Sum_{d divides n} d! ).

%Y Cf. A062796 ( Sum_{d divides n} d^d ), A066108 ( Sum_{d divides n} n^d ).

%K nonn

%O 1,2

%A _Joerg Arndt_, Oct 07 2012