88.32 SFD chains and factorion cycles

@article{Abbott20048832SC,
  title={88.32 SFD chains and factorion cycles},
  author={Stephen Abbott},
  journal={The Mathematical Gazette},
  year={2004},
  volume={88},
  pages={261 - 263}
}
  • S. Abbott
  • Published 1 July 2004
  • Mathematics
  • The Mathematical Gazette
Note that permuting the digits oiN leaves S„ unaffected. A factorion is a number, N, such that S (N) = N. The only factorions are 1, 2, 145 and 40585. In a generalisation analogous to amicable numbers generalising perfect numbers, Gupta defines a pair of amicable factorions as a pair of numbers, (N, M) such that S (N) = M and 5 (M) = N, and claims without proof that (871, 45361) and (872, 45362) are the only amicable factorions. He then considers r-cycles, in which 5(A0 = N, but S (A) * N, for… 

References

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Integers and the Sum of the Factorials of their Digits
88.31 Sum of the factorials of the digits of integers
  • S. Gupta
  • Mathematics
    The Mathematical Gazette
  • 2004
SHY AM SUNDER GUPTA Chief Bridge Engineer
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