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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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2
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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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}]
dnd1Q[n_]:=Count[Divisors[n], _?(DigitCount[n, 2, 1]==DigitCount[ #, 2, 1] == DigitCount[n/#, 2, 1]&)]==1; Select[Range[800000], dnd1Q] (* Harvey P. Dale, Aug 03 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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