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Fermi-Dirac semiprimes: products of two distinct terms of A050376.
6

%I #23 Oct 31 2023 19:21:14

%S 6,8,10,12,14,15,18,20,21,22,26,27,28,32,33,34,35,36,38,39,44,45,46,

%T 48,50,51,52,55,57,58,62,63,64,65,68,69,74,75,76,77,80,82,85,86,87,91,

%U 92,93,94,95,98,99,100,106,111,112,115,116,117,118,119,122

%N Fermi-Dirac semiprimes: products of two distinct terms of A050376.

%C The sequence essentially differs from A000379 beginning with a(108)=212 (not 210). All squarefree terms of A001358 are in the sequence.

%D Vladimir S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences, Vol. 4 (1996), pp. 28-43 [Russian].

%H Peter J. C. Moses, <a href="/A176525/b176525.txt">Table of n, a(n) for n = 1..10000</a>

%H Simon Litsyn and Vladimir 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, Vol. 7 (2007), Article #A33, pp. 1-36.

%F If a(n)=u*v, u<v, u,v are distinct terms of A050376 "Fermi-Dirac primes", then A064380(a(n))=a(n)-u-v+1+Sum{i>=1}(-1)^(i-1)*floor(v/u^i).

%t Select[Range[120], Plus @@ DigitCount[Last /@ FactorInteger[#], 2, 1] == 2 &] (* _Amiram Eldar_, Nov 27 2020 *)

%Y Cf. A001358, A050376, A000379, A176472, A176509, A064380, A050292.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Apr 19 2010, Apr 20 2010

%E Effectively duplicate content (due to duplicate referenced sequence) removed by _Peter Munn_, Dec 19 2019