On a question of Erdős concerning cohesive basic sequences
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- by D. L. Goldsmith and A. A. Gioia PDF
- Proc. Amer. Math. Soc. 34 (1972), 356-358 Request permission
Abstract:
For an arbitrary basic sequence $\mathcal {B}$, set $V(\mathcal {B}) = \{ \# {B_k}|k \in {Z^ + }\}$, where $\# {B_k}$ is the number of pairs (a, b) in $\mathcal {B}$ such that $ab = k$. It is proved that $V(\mathcal {B})$ is unbounded if either $\mathcal {B}$ is cohesive or $\mathcal {B} \not \subset \mathcal {M}$. The set $V(\mathcal {B})$ is determined explicitly in these cases.References
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T. B. Carroll and A. A. Gioia, On extended linear functions, Notices Amer. Math. Soc. 18 (1971), 799. Abstract #71T-A161.
- A. A. Gioia and D. L. Goldsmith, Convolutions of arithmetic functions over cohesive basic sequences, Pacific J. Math. 38 (1971), 391–399. MR 309841, DOI 10.2140/pjm.1971.38.391
- Donald L. Goldsmith, On the density of certain cohesive basic sequences, Pacific J. Math. 42 (1972), 323–327. MR 360510, DOI 10.2140/pjm.1972.42.323
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 356-358
- MSC: Primary 10C10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294285-5
- MathSciNet review: 0294285