Emadian, Elliot R.; Finch-Smith, Carrie E.; Kallus, Margaret G. Ruth-Aaron pairs containing Riesel or Sierpiński numbers. (English) Zbl 1448.11007 Integers 18, Paper A72, 6 p. (2018). Given the prime-power decomposition of an integer \(n=p_1^{e_1}\cdots p_r^{e_r}\) we define \(S(n)=e_1p_1+\cdots +e_rp_r\) the sum (with multiplicities) of its factors. If \(S(n)=S(n+1)\), then \((n,n+1)\) forms a so-called Ruth-Aaron pair.The authors use previous work by Nelson, Penney and Pomerance on these numbers, in which they provided a method to construct such pairs, in order to construct Ruth-Aaron pairs such that at least one of the members is a Riesel or a Sierpinski number. Reviewer: Antonio M. Oller Marcén (Zaragoza) Cited in 1 Document MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11A51 Factorization; primality Keywords:Ruth-Aaron pair; Riesel number; Sierpinski number PDFBibTeX XMLCite \textit{E. R. Emadian} et al., Integers 18, Paper A72, 6 p. (2018; Zbl 1448.11007) Full Text: Link References: [1] C. Nelson, D. E. Penney, and C. Pomerance, 714 and 715, J. Recreat. Math. 7 (1974), no. 2, 87-89. [2] H. Riesel, N˚agra stora primtal, Elementa 39 (1956), 258-260. [3] W. Sierpi´nski, Sur un probl‘eme concernant les nombres k2n+ 1, Elem. Math. 15 (1960), 73-74. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.