Geodesic
Partial sums of powers of prime factors
Journal of integer sequences, Tome 10 (2007) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {De Koninck, Jean-Marie and Luca, Florian},
     title = {Partial sums of powers of prime factors},
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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/