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A272035
Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is an integer.
4
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
1,3
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
LINKS
Peter Kagey, Table of n, a(n) for n = 1..450 (All terms less than 2^30)
EXAMPLE
For n=39, 39_10=100111_2, and 1/1 + 1/2 + 1/3 + 1/6 = 2, an integer.
MATHEMATICA
Select[Range[2^20], IntegerQ@ Total[1/Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]] &] (* Michael De Vlieger, Apr 18 2016 *)
PROG
(PARI) isok(n) = {my(b = Vecrev(binary(n))); denominator(sum(k=1, #b, b[k]/k)) == 1; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 18 2016
STATUS
approved