A272034 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is the inverse of an integer.

1, 2, 4, 8, 16, 32, 36, 38, 64, 128, 256, 512, 1024, 2048, 2056, 2080, 2088, 2090, 4096, 8192, 16384, 16896, 16900, 16902, 16928, 18944, 18952, 18954, 18988, 32768, 65536, 131072, 131328, 131332, 131334, 131360, 133376, 133384, 133386, 133420, 148224, 148256, 148258, 150284

Offset

1,2

Comments

That is, numbers such that A116416(n) is equal to 1.

The powers of 2 (A000079) form a subsequence.

Links

Peter Kagey, Table of n, a(n) for n = 1..354

Example

For n=36, 38_10=100100_2, and 1/3 + 1/6 = 1/2, the inverse of an integer.

Mathematica

Select[Range[2^18], IntegerQ[1/Total[1/# & /@ Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]]] &] (* Michael De Vlieger, Apr 18 2016 *)

Prog

(PARI) isok(n) = {my(b = Vecrev(binary(n))); numerator(sum(k=1, #b, b[k]/k)) == 1; }

Crossrefs

Cf. A000079, A116416, A116417, A272035, A272036, A272081.

Sequence in context: A045603 A072011 A068535 * A356382 A051505 A353720

Adjacent sequences: A272031 A272032 A272033 * A272035 A272036 A272037

Keyword

nonn

Author

Michel Marcus, Apr 18 2016

Status

approved