On relatively prime odd amicable numbers

Author:
Peter Hagis

Journal:
Math. Comp. **23** (1969), 539-543

MSC:
Primary 10.43

MathSciNet review:
0246816

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Abstract: Whether or not a relatively prime pair of amicable numbers exists is still an open question. In this paper some necessary conditions for and to be a pair of odd relatively prime amicable numbers are proved. In particular, lower bounds for , , and the number of prime divisors of are established. The arguments are based on an extensive case study carried out on the CDC 6400 at the Temple University Computing Center.

**[1]**J. Alanen, O. Ore, and J. Stemple,*Systematic computations on amicable numbers*, Math. Comp.**21**(1967), 242–245. MR**0222006**, 10.1090/S0025-5718-1967-0222006-7**[2]**Paul Bratley and John McKay,*More amicable numbers*, Math. Comp.**22**(1968), 677–678. MR**0225706**, 10.1090/S0025-5718-1968-0225706-9**[3]**Edward Brind Escott,*Amicable numbers*, Scripta Math.**12**(1946), 61–72. MR**0017293****[4]**Mariano García,*New amicable pairs*, Scripta Math.**23**(1957), 167–171. MR**0098703****[5]**Peter Hagis Jr.,*Relatively prime amicable numbers of opposite parity*, Math. Mag.**43**(1970), 14–20. MR**0253977****[6]**Hans-Joachim Kanold,*Untere Schranken für teilerfremde befreundete Zahlen*, Arch. Math. (Basel)**4**(1953), 399–401 (German). MR**0058622****[7]**Elvin J. Lee,*Amicable numbers and the bilinear diophantine equation*, Math. Comp.**22**(1968), 181–187. MR**0224543**, 10.1090/S0025-5718-1968-0224543-9**[8]**P. Poulet, "43 new couples of amicable numbers,"*Scripta Math.*, v. 14, 1948, p. 77.

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0246816-7

Article copyright:
© Copyright 1969
American Mathematical Society