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A087207
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A binary representation of the primes that divide a number.
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1
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0, 1, 2, 1, 4, 3, 8, 1, 2, 5, 16, 3, 32, 9, 6, 1, 64, 3, 128, 5, 10, 17, 256, 3, 4, 33, 2, 9, 512, 7, 1024, 1, 18, 65, 12, 3, 2048, 129, 34, 5, 4096, 11, 8192, 17, 6, 257, 16384, 3, 8, 5, 66, 33, 32768, 3, 20, 9, 130, 513, 65536, 7, 131072, 1025, 10, 1, 36, 19, 262144, 65, 258
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The binary representation of a(n) shows which prime numbers divide n, but not the multiplicities. a(2)=1, a(3)=10, a(4)=1, a(5)=100, a(6)=11, a(10)=101, a(30)=111, etc.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| Additive with a(p^e) = 2^pi(p-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 29 2003
a(n) gives the m such that A019565(m) = A007947(n). - Naohiro Nomoto
A000120(a(n)) = A001221(n); a(n) = Sum(2^(A049084(p)-1): p prime-factor of n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2003
G.f. sum(k>=1, 2^(k-1)*x^prime(k)/(1-x^prime(k)). [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 01 2009]
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EXAMPLE
| a(140) = 13, binary 1101 because 140 is divisible by the first, third and fourth primes and 2^(1-1) + 2^(3-1) + 2^(4-1) = 13.
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MATHEMATICA
| a[n_] := Total[ 2^(PrimePi /@ FactorInteger[n][[All, 1]] - 1)]; a[1] = 0; Table[a[n], {n, 1, 69}] (* From Jean-François Alcover, Dec 12 2011 *)
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CROSSREFS
| Cf. A000040.
Sequence in context: A138236 A058354 A085930 * A179206 A074987 A128280
Adjacent sequences: A087204 A087205 A087206 * A087208 A087209 A087210
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KEYWORD
| nonn,nice
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AUTHOR
| Mitch Cervinka (puritan(AT)planetkc.com), Oct 26 2003
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EXTENSIONS
| More terms from Don Reble (djr(AT)nk.ca), Ray Chandler (rayjchandler(AT)sbcglobal.net) and Naohiro Nomoto (pcmusume(AT)alpha-net.ne.jp), Oct 28 2003
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