A272035 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is an integer.

0, 1, 38, 39, 2090, 2091, 16902, 16903, 18954, 18955, 18988, 18989, 131334, 131335, 133386, 133387, 133420, 133421, 148258, 148259, 150284, 150285, 524314, 524315, 524348, 524349, 526386, 526387, 541212, 541213, 543250, 543251, 543284, 543285, 655644, 655645, 657682

Offset: 1

Author

Michel Marcus, Apr 18 2016

Keywords

• nonn

Comments

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

2k is in this sequence if and only if 2k + 1 is. Therefore n + a(n) is odd for all n. - Peter Kagey, Apr 19 2016

Examples

			For n=39, 39_10=100111_2, and 1/1 + 1/2 + 1/3 + 1/6 = 2, an integer.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..450 (All terms less than 2^30)

Crossrefs

Cf. A116416, A116417, A272034, A272036, A272082.

Programs

Mathematica

Select[Range[2^20], IntegerQ@ Total[1/Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]] &] (* Michael De Vlieger, Apr 18 2016 *)

PARI

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