论文信息 - On phi-amicable pairs

On phi-amicable pairs

Let o(n) denote Euler's totient function, i.e., the number of positive integers 1. We call these numbers o-amicable pairs with multiplier k, analogously to Carmichael's multiply amicable pairs for the σ-function (which sums all the divisors of n). We have computed all the o-amicable pairs with larger member 10 9 , the largest pair consisting of two 46-digit numbers.

Herman J. J. te Riele | Graeme L. Cohen

[1] Jan P. Hogendijk,et al. Notes on Thabit ibn Qurra and his rule for amicable numbers , 1989 .

[2] W. Borho. Some large primes and amicable numbers , 1981 .

[3] Hendrik Jager,et al. Number Theory Noordwijkerhout 1983 , 1984 .

[4] Miriam Hausman. The Solution of a Special Arithmetic Equation , 1982, Canadian Mathematical Bulletin.

[5] H. J. J. te Riele,et al. Computation of all the amicable paris below 10 10 , 1986 .

[6] R. Guy. Unsolved Problems in Number Theory , 1981 .

[7] Thomas E. Mason. On Amicable Numbers and their Generalizations , 1921 .

[8] Herman J. J. te Riele,et al. New very large amicable pairs , 1984 .

[9] Graeme L. Cohen,et al. On $ \phi $ -amicable pairs (with appendix) , 1995 .

[10] te Herman Riele. Computation of all the amicable pairs below $10sp {10}$. With a supplement , 1985 .