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Search: id:A080026
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| A080026 |
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Numbers n having exactly one divisor d such that in binary representation d and n/d have the same number of 1's as n. |
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+0
3
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| 1, 9, 49, 225, 961, 3969, 6241, 8281, 16129, 24649, 25281, 33489, 34969, 65025, 82369, 100489, 101761, 123201, 133225, 140625, 143641, 198025, 261121, 328329, 330625, 405769, 408321, 494209, 540225, 564001, 576081, 582169, 664225, 797449
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)=m^2 with A000120(m)=A000120(n).
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EXAMPLE
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6241=79^2: 1100001100001=1001111*1001111, therefore 6241 is a term.
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MATHEMATICA
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Do[b = Count[ IntegerDigits[n^2, 2], 1]; If[ Count[ IntegerDigits[n, 2], 1] == b, c = 0; d = IntegerDigits[ Divisors[n^2], 2]; l = DivisorSigma[0, n^2]; k = 1; While[ k < Ceiling[l/2], If[Count[d[[k]], 1] == b && Count[d[[l - k + 1]], 1] == b, c++ ]; k++ ]; If[c == 0, Print[n^2]]], {n, 1, 1000}]
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CROSSREFS
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Cf. A007088, A000120, A000005, A000196, A000290.
A080024(a(n))=1, subsequence of A080025.
Sequence in context: A027608 A003297 A012248 this_sequence A060867 A081655 A146798
Adjacent sequences: A080023 A080024 A080025 this_sequence A080027 A080028 A080029
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 21 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 24 2003
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