On amicable and sociable numbers

Author:
Henri Cohen

Journal:
Math. Comp. **24** (1970), 423-429

MSC:
Primary 10.03

DOI:
https://doi.org/10.1090/S0025-5718-1970-0271004-6

MathSciNet review:
0271004

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Abstract | References | Similar Articles | Additional Information

Abstract: An exhaustive search has yielded 236 amicable pairs of which the lesser number is smaller than , 57 pairs being new.

It has also yielded 9 new sociable groups of order 10 or less, of which the lesser number is smaller than ; the 9 sociable groups are all of order 4.

The sequence of iterates of the function starting with 276 has also been extended to 119 terms.

**[1]**Edward Brind Escott,*Amicable numbers*, Scripta Math.**12**(1946), 61–72. MR**0017293****[2]**P. Poulet, "43 new couples of amicable numbers,"*Scripta Math.*, v. 14. 1948. p. 77.**[3]**Mariano García,*New amicable pairs*, Scripta Math.**23**(1957), 167–171. MR**0098703****[4]**Elvin J. Lee,*Amicable numbers and the bilinear diophantine equation*, Math. Comp.**22**(1968), 181–187. MR**0224543**, https://doi.org/10.1090/S0025-5718-1968-0224543-9**[5]**E. J. Lee, "The discovery of amicable numbers,"*J. Recreational Math.*(To appear.)**[6]**J. Alanen, O. Ore, and J. Stemple,*Systematic computations on amicable numbers*, Math. Comp.**21**(1967), 242–245. MR**0222006**, https://doi.org/10.1090/S0025-5718-1967-0222006-7**[7]**Paul Bratley and John McKay,*More amicable numbers*, Math. Comp.**22**(1968), 677–678. MR**0225706**, https://doi.org/10.1090/S0025-5718-1968-0225706-9**[8]**P. Poulet,*L'intermédiaire des math.*, v. 25, 1918, pp. 100-101.**[9]**G. A. Paxson,*Annapolis Meeting of the Mathematical Association of America*, May 5th 1956.**[10]**L. E. Dickson, "Theorems and tables on the sum of the divisors of a number,"*Quart. J. Math.*, v. 44. 1913, pp. 264-296.**[11]**P. Erdös,*On amicable numbers*, Publ. Math. Debrecen**4**(1955), 108–111. MR**0069198**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0271004-6

Keywords:
Amicable numbers,
sociable numbers,
aliquot series

Article copyright:
© Copyright 1970
American Mathematical Society