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Multiperfect numbers with identical digits
Authors:Florian Luca
Affiliation:Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA
Abstract:Let g?2. A natural number N is called a repdigit in base g if all of the digits in its base g expansion are equal, i.e., if View the MathML source for some m?1 and some D∈{1,2,…,g−1}. We call N perfect if σ(N)=2N, where σ denotes the usual sum-of-divisors function. More generally, we call N multiperfect if σ(N) is a proper multiple of N. The second author recently showed that for each fixed g?2, there are finitely many repdigit perfect numbers in base g, and that when g=10, the only example is N=6. We prove the same results for repdigit multiperfect numbers.
Keywords:11A25   11B39
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