Odd sturdy numbers.
1, 3, 5, 7, 9, 15, 17, 21, 31, 33, 35, 45, 49, 51, 63, 65, 69, 73, 75, 85, 89, 93, 105, 127, 129, 133, 135, 153, 155, 161, 165, 189, 195, 217, 225, 255, 257, 259, 261, 267, 273, 275, 279, 315, 341, 381, 385, 403, 441, 455, 465, 511, 513, 515, 517, 525, 527
1
Numbers in this sequence multiplied by 2^k, for any positive k, produce the even sturdy numbers. The Mathematica program is simple, but slow. Faster programs are more complex.
T. D. Noe, Plot of 794 terms (< 2^16)
T. D. Noe, Table of 794 terms (< 2^16)
(Mma) Bits[n_Integer] := Count[IntegerDigits[n, 2], 1]; FlimsyQ[n_Integer] := FlimsyQ[n] = Module[{res, b = Bits[n], k}, If[b <= 2, False, If[EvenQ[n], FlimsyQ[n/2], res = Union[Mod[2^Range[n], n]]; If[Length[res] == n - 1, True, k = 2; While[k < b && ! MemberQ[Union[Mod[Plus @@@ Subsets[res, {k}], n]], 0], k++]; k < b]]]]; Select[Range[1, 400, 2], ! FlimsyQ[#] &]
Cf. A125121, S000849 (even sturdy numbers).
nonn,base
T. D. Noe, Feb 09 2016