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%I #15 Apr 04 2024 07:52:18
%S 1,2,5,1,65,326,1957,137,109601,986410,9864101,27126278,7704505,
%T 16926797486,236975164805,888656868019,56874039553217,966858672404690,
%U 17403456103284421,826664164906010,6613313319248080001,138879579704209680022,3055350753492612960485
%N Squarefree part of the total number of arrangements of a set with n elements.
%H F. Luca and I. E. Shparlinski, <a href="https://doi.org/10.1017/S0017089507003734">On the squarefree parts of floor(e*n!)</a>, Glasgow Math. J., 49 (2007), 391-403.
%F a(n) = core(A000522(n)).
%p A000522 := proc(n)
%p add( n!/k!,k=0..n) ;
%p end proc:
%p A222637 := proc(n)
%p A007913(A000522(n)) ;
%p end proc: # _R. J. Mathar_, Jan 16 2014
%t core[n_] := Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[n]);
%t a[n_] := If[n == 0, 1, core[Floor[E*n!]]];
%t Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Apr 04 2024 *)
%o (PARI) a(n) = core(n! * polcoeff(exp(x + x*O(x^n)) / (1 - x), n))
%Y Cf. A000522, A007913, A222638, A222639.
%K nonn
%O 0,2
%A _Michel Marcus_, Feb 27 2013
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