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%I #14 Jul 14 2020 07:40:45
%S 1,1,1,4,1,1,1,10,1,1,1,2,13,1,1,2,1,1,1,20,1,1,1,58,1,1,1,2,1,1,1,2,
%T 5,1,1,4,1,1,1,2,1,1,1,2,5,1,1,2,1,1,1,8,1,1,1,2,1,5,1,2,1,1,1,2,23,1,
%U 1,4,1,5,1,2,1,37
%N Square root of the square 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) = sqrt(A000522(n)/core(A000522(n))).
%o (PARI) a(n) = core(n! * polcoeff(exp(x + x*O(x^n)) / (1 - x), n), 1)[2]
%Y Cf. A000188, A000522, A007913, A222637.
%K nonn
%O 0,4
%A _Michel Marcus_, Feb 27 2013
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