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A131850
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Odious 3-almost primes.
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1
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8, 28, 42, 44, 50, 52, 70, 76, 98, 110, 117, 124, 138, 148, 164, 171, 174, 182, 186, 188, 230, 236, 242, 244, 261, 266, 268, 273, 279, 285, 286, 290, 292, 310, 316, 322, 333, 345, 357, 369, 370, 385, 388, 406, 410, 412, 425, 426, 428, 434, 436, 465, 475, 477
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OFFSET
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1,1
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COMMENTS
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Numbers that are divisible by exactly 3 primes (counted with multiplicity) and also odious (odd number of 1's in binary expansion). This is to 3-almost primes A014612 as A027697 is to primes A000040 and as semiprimes not in A130593 are to semiprimes A001358. 3-almost primes that are not odious are evil A001969.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 8 because 8 = 2^3 is divisible by exactly 3 primes (counted with multiplicity and 8 (base 2) = 1000 has an odd number (1) of ones in its binary expansion.
a(2) = 28 = 2^2 * 7 = 11100 (base 2) has an odd number (1) of ones in its binary expansion.
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MAPLE
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isA014612 := proc(n) if numtheory[bigomega](n) = 3 then true ; else false ; fi ; end: isA000069 := proc(n) bdigs := convert(n, base, 2) ; if add(i, i=bdigs) mod 2 = 1 then true; else false ; fi ; end: isA131850 := proc(n) isA000069(n) and isA014612(n) ; end: for n from 1 to 500 do if isA131850(n) then printf("%d, ", n) fi ; od: # R. J. Mathar, Oct 24 2007
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MATHEMATICA
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Select[Range[500], PrimeOmega[#]==3&&OddQ[DigitCount[#, 2, 1]]&] (* Harvey P. Dale, Jun 11 2017 *)
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PROG
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(PARI) list(lim)=my(v=List(), t); forprime(p=2, lim\4, forprime(q=2, min(lim\(2*p), p), t=p*q; forprime(r=2, min(lim\t, q), if(hammingweight(t*r)%2, listput(v, t*r))))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Mar 29 2013
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CROSSREFS
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KEYWORD
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easy,nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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