A331832 - OEIS

%I #8 Jan 29 2020 01:42:07

%S 1,3,9,11,23,29,33,41,43,47,53,59,69,71,83,89,101,103,109,113,129,131,

%T 137,139,149,151,157,163,181,191,197,199,211,227,233,239,249,251,263,

%U 269,281,283,293,307,311,317,331,349,353,367,373,379,383,389,397,401

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

%H Amiram Eldar, <a href="/A331832/b331832.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 is a term since all of its divisors, 1, 3 and 9, or 1, 111, and 11001 in negabinary representation, have an odd number of 1's.

%t negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; odNegaBinQ[n_] := OddQ[negaBinWt[n]]; seqQ[n_] := AllTrue[Divisors[n], odNegaBinQ]; Select[Range[401],seqQ]

%Y Subsequence of A268273.

%Y Cf. A027615, A039724, A093696.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Jan 28 2020