OFFSET
1,1
COMMENTS
For a denominator with an exponent base of 2, this series is A000027; for bases more than 3, no integer values are known. All powers of 2 greater than 2 are believed to be in this sequence. - Drake Thomas, May 13 2016
LINKS
RavenclawPrefect, When is Sum_{k>=0} k^n/3^k an integer?
EXAMPLE
4 is in the list because 0^4/3^0 + 1^4/3^1 + 2^4/3^2 + ... = 15 is an integer.
MATHEMATICA
Select[Range@ 260, IntegerQ[Sum[k^#/3^k, {k, 0, Infinity}]] &] (* Michael De Vlieger, Sep 02 2015 *)
Select[Range @ 260, IntegerQ@ HurwitzLerchPhi[1/3, -#, 0] &] (* Giovanni Resta, Sep 10 2015, fixed by Vaclav Kotesovec, Mar 23 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Hagen von Eitzen, Sep 01 2015
STATUS
approved