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《Journal of Anhui Normal University(Natural Science)》 1991-04
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A Bound for the Number of Multiplicative Partitions and Additive Partitions

Teng Degui (Anhui Institute of Education)  
Let n be a pasitive integer, p(n) (f(n)) denotes the number of additive (multiplicative) partitions of n. Fn denotes the n-th of Fibonacci Sequence. In this paper:(Ⅰ)We have obtained recursion formula of Caculating f(n)(Ⅱ) We proved: p(n)≤Fn+1, f(n)≤2/3n and f(n)≤n/(logn) (n≠144)Therefore, we have answered the conjectured of J. H. Hughes and J. O. Shallit for f(n)≤nand f(n)≤n/(logn)(n≠144).
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