The number of distinct subsums of

Authors:
M. N. Bleicher and P. Erdős

Journal:
Math. Comp. **29** (1975), 29-42

MSC:
Primary 10A25

DOI:
https://doi.org/10.1090/S0025-5718-1975-0366795-4

MathSciNet review:
0366795

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we improve the lower bounds for the number, , of distinct values obtained as subsums of the first *N* terms of the harmonic series. We obtain a bound of the form

*e*.

**[1]**M. N. Bleicher,*A new algorithm for the expansion of Egyptian fractions*, J. Number Theory**4**(1972), 342–382. MR**0323696**, https://doi.org/10.1016/0022-314X(72)90069-8**[2]**M. N. BLEICHER & P. ERDÖS, "Denominators of Egyptian fractions. II" (To appear.)**[3]**M. N. BLEICHER & P. ERDÖS, "The number of distinct subsums of*Notices Amer. Math. Soc.*, v. 20, 1973. Abstract #706-10-3.**[4]**J. Barkley Rosser and Lowell Schoenfeld,*Approximate formulas for some functions of prime numbers*, Illinois J. Math.**6**(1962), 64–94. MR**0137689**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0366795-4

Keywords:
Harmonic series,
squarefree integers,
prime numbers,
distinct subsums

Article copyright:
© Copyright 1975
American Mathematical Society