A080026 - OEIS

%I #8 Aug 03 2021 16:28:05

%S 1,9,49,225,961,3969,6241,8281,16129,24649,25281,33489,34969,65025,

%T 82369,100489,101761,123201,133225,140625,143641,198025,261121,328329,

%U 330625,405769,408321,494209,540225,564001,576081,582169,664225,797449

%N 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.

%C a(n)=m^2 with A000120(m)=A000120(n).

%e 6241=79^2: 1100001100001=1001111*1001111, therefore 6241 is a term.

%t 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}]

%t 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 *)

%Y Cf. A007088, A000120, A000005, A000196, A000290.

%Y A080024(a(n))=1, subsequence of A080025.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jan 21 2003

%E More terms from _Robert G. Wilson v_, Jan 24 2003