A331833 Numbers k such that all the divisors of k, excluding 1, have an even number of 1's in their negabinary representations.
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
Offset: 1
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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]