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

Author

Michel Marcus, Apr 18 2016

Keywords

• nonn

Comments

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

The powers of 2 (A000079) form a subsequence.

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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