A261811 Numbers m such that Sum_{k>=0} k^m/3^k is an integer.

4, 8, 12, 13, 16, 20, 24, 32, 36, 40, 44, 48, 52, 56, 64, 68, 72, 76, 77, 80, 84, 88, 96, 100, 104, 108, 112, 116, 120, 122, 128, 132, 136, 140, 141, 144, 148, 152, 160, 164, 168, 172, 176, 180, 184, 192, 196, 200, 204, 205, 208, 212, 216, 224, 228, 232, 236, 240, 244, 248, 256, 260

Offset: 1

Author

Hagen von Eitzen, Sep 01 2015

Keywords

• nonn

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

Examples

			4 is in the list because 0^4/3^0 + 1^4/3^1 + 2^4/3^2 + ... = 15 is an integer.
		

Links

• RavenclawPrefect, When is Sum_{k>=0} k^n/3^k an integer?

Programs

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 *)