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A080024
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Number of divisors d of n such that in binary representation d and n/d have the same number of 1's as n.
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2
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1, 2, 0, 3, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 5, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)<=A000005(n), a(n)=A000005(n) iff n=2^k (A000079).
Not multiplicative. Counterexample: 441=3^2*7^2, a(441)=0, but a(3^2) = a(7^2) = 1. Christian G. Bower (bowerc(AT)usa.net) May 16, 2005.
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EXAMPLE
| Divisors of 36 = {1,2,3,4,6,9,12,18,36}, 36->100100 and also 3,6,12 have two 1's in binary notation with 36=3*12=6*6, therefore a(36)=3 (18->10010 doesn't count, as 36/18=2->10 has only one binary 1).
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CROSSREFS
| Cf. A007088, A000120, a(A080025(n))>0, a(A080026(n))=1.
Sequence in context: A114511 A085199 A085200 * A035199 A035229 A109362
Adjacent sequences: A080021 A080022 A080023 * A080025 A080026 A080027
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 21 2003
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