This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A176699 Fermi-Dirac composite numbers that are not a sum of two Fermi-Dirac primes (A050376). 1


%S 145,187,205,217,219,221,247,301,325,343,415,427,475,517,535,553,555,

%T 583,637,667,671,697,715,781,783,793,795,805,807,817,835,847,851,871,

%U 895,901

%N Fermi-Dirac composite numbers that are not a sum of two Fermi-Dirac primes (A050376).

%C We define a Fermi-Dirac composite number as a positive integer with at least two factors in its factorization over distinct terms of A050376.

%C They are those c for which A064547(c) >=2, namely c= 6, 8, 10, 12,..., 62, 63, 64, 65, ..., or the complement of A050376 with respect to the natural numbers >1.

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

%H S. Litsyn and V. Shevelev, <a href="http://www.emis.de/journals/INTEGERS/papers/h33/h33.Abstract.html">On factorization of integers with restrictions on the exponents</a>, INTEGERS: El. J. of Combin. Number Theory, 7(2007), #A33,1-35

%e 291=3*97 is a Fermi-Dirac composite number, equal to 289+2, the sum of two Fermi-Dirac primes. Therefore 291 is not in the sequence.

%p A064547 := proc(n) f := ifactors(n)[2] ; a := 0 ; for p in f do a := a+wt(op(2, p)) ; end do: a ; end proc:

%p A050376 := proc(n) local a; if n = 1 then 2; else for a from procname(n-1)+1 do if A064547(a) = 1 then return a; end if; end do: end if; end proc:

%p isA176699 := proc(n) local pi,q ; if A064547(n) < 2 then return false; end if; for pi from 1 do if A050376(pi) > n then return true; else q := n-A050376(pi) ; if A064547(q) = 1 then return false; end if; end if; end do; end proc:

%p for n from 2 to 1000 do if isA176699(n) then printf("%d,\n",n) ; end if; end do: # R. J. Mathar, Jun 160 2010

%Y Cf. A050376, A025583, A164376.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Apr 24 2010, Apr 26 2010

%E Edited and extended by _R. J. Mathar_, Jun 16 2010

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 29 16:08 EST 2015. Contains 264661 sequences.