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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.
4
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 18 2016
STATUS
approved