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Search: id:A140707
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| A140707 |
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A positive integer n is included if n written in binary contains the same number of 0's as the number of distinct primes that divide n. |
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+0
1
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| 1, 2, 5, 10, 11, 12, 13, 21, 22, 23, 26, 27, 28, 29, 39, 42, 45, 46, 47, 51, 54, 57, 58, 59, 61, 78, 87, 90, 91, 93, 94, 102, 105, 114, 115, 117, 118, 120, 122, 124, 125, 159, 174, 175, 182, 183, 186, 187, 189, 191, 207, 210, 215, 219, 220, 221, 223, 230, 234, 235
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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{n: A080791(n)= A001221(n)}. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008]
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EXAMPLE
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90 written in binary is 1011010. There are three 0s in this binary representation. 90 has the prime factorization: 2^1 *3^2 *5^1. There are 3 distinct primes dividing 90. Since the number of 0s in the binary representation equals the number of distinct primes dividing 90, then 90 is in the sequence.
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MAPLE
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A080791 := proc(n) local dgs ; dgs := convert(n, base, 2) ; nops(dgs)-add(i, i=dgs) ; end: A001221 := proc(n) nops(numtheory[factorset](n)) ; end: isA140707 := proc(n) RETURN( A080791(n) = A001221(n)) ; end: for n from 1 to 300 do if isA140707(n) then printf("%d, ", n) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008]
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CROSSREFS
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Cf. A071594, A001221, A023416, .
Sequence in context: A138848 A123466 A144793 this_sequence A136817 A140180 A056704
Adjacent sequences: A140704 A140705 A140706 this_sequence A140708 A140709 A140710
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KEYWORD
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base,nonn
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AUTHOR
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Leroy Quet Jul 11 2008
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EXTENSIONS
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Extended beyond 42 by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008
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