

A331833


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


1



1, 2, 5, 7, 10, 13, 14, 17, 19, 25, 31, 34, 37, 49, 61, 62, 65, 67, 73, 79, 85, 97, 107, 127, 133, 155, 167, 170, 173, 179, 193, 214, 217, 223, 229, 241, 247, 254, 257, 259, 271, 277, 289, 310, 313, 325, 334, 337, 347, 359, 365, 395, 419, 425, 427, 431, 434, 443
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

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


EXAMPLE

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.


MATHEMATICA

negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n1, 2]] + Mod[n, 2]]; eveNegaBinQ[n_] := EvenQ[negaBinWt[n]]; seqQ[n_] := AllTrue[Rest @ Divisors[n], eveNegaBinQ]; Select[Range[401], seqQ]


CROSSREFS

Subsequence of A268272.
Cf. A027615, A039724, A093688.
Sequence in context: A298869 A219666 A026340 * A018717 A188036 A292645
Adjacent sequences: A331830 A331831 A331832 * A331834 A331835 A331836


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Jan 28 2020


STATUS

approved



