

A331832


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

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


EXAMPLE

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.


MATHEMATICA

negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n1, 2]] + Mod[n, 2]]; odNegaBinQ[n_] := OddQ[negaBinWt[n]]; seqQ[n_] := AllTrue[Divisors[n], odNegaBinQ]; Select[Range[401], seqQ]


CROSSREFS

Subsequence of A268273.
Cf. A027615, A039724, A093696.
Sequence in context: A105949 A302422 A032665 * A032915 A019080 A060141
Adjacent sequences: A331829 A331830 A331831 * A331833 A331834 A331835


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Jan 28 2020


STATUS

approved



