A331833 - OEIS

%I #8 Jan 29 2020 01:42:04

%S 1,2,5,7,10,13,14,17,19,25,31,34,37,49,61,62,65,67,73,79,85,97,107,

%T 127,133,155,167,170,173,179,193,214,217,223,229,241,247,254,257,259,

%U 271,277,289,310,313,325,334,337,347,359,365,395,419,425,427,431,434,443

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

%H Amiram Eldar, <a href="/A331833/b331833.txt">Table of n, a(n) for n = 1..10000</a>

%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.

%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]

%Y Subsequence of A268272.

%Y Cf. A027615, A039724, A093688.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Jan 28 2020