A note on the Catalan-Dickson conjecture

Author:
H. J. J. te Riele

Journal:
Math. Comp. **27** (1973), 189-192

MSC:
Primary 10A40

DOI:
https://doi.org/10.1090/S0025-5718-1973-0325522-5

Corrigendum:
Math. Comp. **27** (1973), 1011-1012.

MathSciNet review:
0325522

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, the existence of an aliquot sequence with more than 5092 monotonically increasing even terms is proved; the first 125 terms are listed.

**[1]**J. D. Alanen,*Empirical Study of Aliquot Series*, Ph.D. Thesis, Yale University, New Haven, Conn., 1972.**[2]**E. Catalan,*Propositions et questions diverses*, Bull. Soc. Math. France**16**(1888), 128–129 (French). MR**1504036****[3]**Henri Cohen,*On amicable and sociable numbers*, Math. Comp.**24**(1970), 423–429. MR**0271004**, https://doi.org/10.1090/S0025-5718-1970-0271004-6**[4]**L. E. Dickson, "Theorems and tables on the sum of the divisors of a number,"*Quart. J. Pure Appl. Math.*, v. 44, 1913, pp. 264-296.**[5]**Richard K. Guy and J. L. Selfridge,*Interim report on aliquot series*, Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971) Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971, pp. 557–580. MR**0335412****[6]**D. H. Lehmer, private communication.**[7]**G. A. Paxson,*Annapolis meeting of the Math. Assoc. of America*, May 5th, 1956.**[8]**Bryant Tuckerman,*The 24th Mersenne prime*, Proc. Nat. Acad. Sci. U.S.A.**68**(1971), 2319–2320. MR**0291072**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0325522-5

Keywords:
Aliquot sequence,
Catalan-Dickson conjecture

Article copyright:
© Copyright 1973
American Mathematical Society