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Search: id:A131850
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| A131850 |
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Odious 3-almost primes. |
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+0
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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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FORMULA
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A014612 INTERSECTION A000069.
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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 (mathar(AT)strw.leidenuniv.nl), Oct 24 2007
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CROSSREFS
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Cf. A000069, A014612.
Sequence in context: A006377 A121739 A166729 this_sequence A009504 A001486 A045850
Adjacent sequences: A131847 A131848 A131849 this_sequence A131851 A131852 A131853
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KEYWORD
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easy,nonn,less
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 04 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2007
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