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A176699 Fermi-Dirac composite numbers that are not a sum of two Fermi-Dirac primes (A050376). 3
145, 187, 205, 217, 219, 221, 247, 301, 325, 343, 415, 427, 475, 517, 535, 553, 555, 583, 637, 667, 671, 697, 715, 781, 783, 793, 795, 805, 807, 817, 835, 847, 851, 871, 895, 901 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..36.

S. Litsyn and V. Shevelev, On factorization of integers with restrictions on the exponents, INTEGERS: El. J. of Combin. Number Theory, 7(2007), #A33,1-35

EXAMPLE

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.

MAPLE

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:

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:

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:

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

CROSSREFS

Cf. A050376, A025583, A164376.

Sequence in context: A159777 A326258 A051414 * A177223 A318530 A158133

Adjacent sequences:  A176696 A176697 A176698 * A176700 A176701 A176702

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Apr 24 2010, Apr 26 2010

EXTENSIONS

Edited and extended by R. J. Mathar, Jun 16 2010

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)