Geodesic
Partial sums of powers of prime factors
Journal of integer sequences, Tome 10 (2007) no. 1
Given integers $k\ge 2$ and $\ell\ge 3$, let $S_{k,\ell}^*$ stand for the set of those positive integers $n$ which can be written as $n=p_1^k+p_2^k+\ldots+p_\ell^k$, where $p_1,p_2,\ldots,p_\ell$ are distinct prime factors of $n$. We study the properties of the sets $S^*_{k,\ell}$ and we show in particular that, given any odd $\ell\ge 3, \displaystyle{\char93 \bigcup_{k=2}^\infty S_{k,\ell}^*=+\infty}$.
Classification : 11A41, 11A25
Keywords: prime factorization 
@article{JIS_2007__10_1_a7,
     author = {De Koninck,  Jean-Marie and Luca,  Florian},
     title = {Partial sums of powers of prime factors},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {1},
     zbl = {1123.11002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a7/}
}
TY  - JOUR
AU  - De Koninck,  Jean-Marie
AU  - Luca,  Florian
TI  - Partial sums of powers of prime factors
JO  - Journal of integer sequences
PY  - 2007
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a7/
LA  - en
ID  - JIS_2007__10_1_a7
ER  - 
%0 Journal Article
%A De Koninck,  Jean-Marie
%A Luca,  Florian
%T Partial sums of powers of prime factors
%J Journal of integer sequences
%D 2007
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a7/
%G en
%F JIS_2007__10_1_a7
De Koninck,  Jean-Marie; Luca,  Florian. Partial sums of powers of prime factors. Journal of integer sequences, Tome 10 (2007) no. 1. http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a7/