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Numbers k such that all the divisors of k, excluding 1, have an even number of 1's in their negabinary representations.

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`%I #8 Jan 29 2020 01:42:04
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`%S 1,2,5,7,10,13,14,17,19,25,31,34,37,49,61,62,65,67,73,79,85,97,107,
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`%T 127,133,155,167,170,173,179,193,214,217,223,229,241,247,254,257,259,
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`%U 271,277,289,310,313,325,334,337,347,359,365,395,419,425,427,431,434,443
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`%N Numbers k such that all the divisors of k, excluding 1, have an even number of 1's in their negabinary representations.
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`%H Amiram Eldar, <a href="/A331833/b331833.txt">Table of n, a(n) for n = 1..10000</a>
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`%e 10 is a term since all of its divisors exclusing 1, i.e., 2, 5 and 10, or 110, 101, and 11110 in negabinary representation, have an even number of 1's.
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`%t negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; eveNegaBinQ[n_] := EvenQ[negaBinWt[n]]; seqQ[n_] := AllTrue[Rest @ Divisors[n], eveNegaBinQ]; Select[Range[401],seqQ]
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`%Y Subsequence of A268272.
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`%Y Cf. A027615, A039724, A093688.
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`%K nonn,base
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`%O 1,2
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`%A _Amiram Eldar_, Jan 28 2020
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