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%I #18 Jun 28 2014 05:12:46
%S 7,8,9,13,18,22,37,57,71
%N Numbers n for which in the factorization of n! over distinct terms of A050376, the numbers of prime and nonprime terms are equal.
%C a(10), if it exists, should be more than 5000. Is a(9)=71 the last term of sequence? - _Peter J. C. Moses_, Apr 19 2014
%C One can prove that a(9)=71 indeed is the last term of this sequence. - _Vladimir Shevelev_, Apr 19 2014.
%D V. S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 [Russian].
%H S. Litsyn and V. S. Shevelev, <a href="http://www.emis.de/journals/INTEGERS/papers/h33/h33.Abstract.html">On factorization of integers with restrictions on the exponent</a>, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 1-36.
%e 7 is in the sequence, since 7! in the considered factorization is 5*7*9*16, and here we have 2 primes and 2 nonprimes.
%Y Cf. A177329, A177333, A177334, A240537, A240606, A240619, A240620, A240668, A240669, A240670, A240672, A240695, A240751, A240755, A240764, A240905, A240906, A241123, A241124, A241139, A241148.
%K nonn,fini,full
%O 1,1
%A _Vladimir Shevelev_, Apr 18 2014
%E Terms a(7) - a(9) from _Peter J. C. Moses_, Apr 19 2014
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