A272034 - OEIS

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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

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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 *)