A331832 Numbers k such that all the divisors of k have an odd number of 1's in their negabinary representations.

1, 3, 9, 11, 23, 29, 33, 41, 43, 47, 53, 59, 69, 71, 83, 89, 101, 103, 109, 113, 129, 131, 137, 139, 149, 151, 157, 163, 181, 191, 197, 199, 211, 227, 233, 239, 249, 251, 263, 269, 281, 283, 293, 307, 311, 317, 331, 349, 353, 367, 373, 379, 383, 389, 397, 401

Offset: 1

Author

Amiram Eldar, Jan 28 2020

Keywords

• nonn
• base

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A268273.

Cf. A027615, A039724, A093696.

Programs

Mathematica

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]