On relatively prime odd amicable numbers

Author:
Peter Hagis

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

MSC:
Primary 10.43

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

MathSciNet review:
0246816

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 & J. Stemple, "Systematic computations on amicable numbers,"*Math. Comp.*, v. 21, 1967, pp. 242-245. MR**36**#5058. MR**0222006 (36:5058)****[2]**P. Bratley & J. McKay, "More amicable numbers,"*Math. Comp.*, v. 22, 1968, pp. 677- 678. MR**37**#1299. MR**0225706 (37:1299)****[3]**E. B. Escott, "Amicable numbers,"*Scripta Math.*, v. 12, 1946, pp. 61-72. MR**8**, 135. MR**0017293 (8:135a)****[4]**M. Garcia, "New amicable pairs,"*Scripta Math.*, v. 23, 1957, pp. 161-171. MR**20**#5158. MR**0098703 (20:5158)****[5]**P. Hagis, Jr., "Relatively prime amicable numbers of opposite parity,"*Math. Mag.*(To appear. ) MR**0253977 (40:7190)****[6]**H.-J. Kanold, "Untere Schranken für teilerfremde befreudete Zahlen,"*Arch Math.*, v. 4, 1953, pp. 399-401. MR**15**, 400. MR**0058622 (15:400i)****[7]**E. J. Lee, "Amicable numbers and the bilinear diophantine equation,"*Math. Comp.*, v. 22, 1968, pp. 181-187. MR**37**#142. MR**0224543 (37:142)****[8]**P. Poulet, "43 new couples of amicable numbers,"*Scripta Math.*, v. 14, 1948, p. 77.

Retrieve articles in *Mathematics of Computation*
with MSC:
10.43

Retrieve articles in all journals with MSC: 10.43

Additional Information

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

Article copyright:
© Copyright 1969
American Mathematical Society