JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 2, Pages 377 - 383
(August 2005)
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SOME IDENTITIES CONCERNING PARTITION FUNCTIONS AND DIVISOR SUMS
Neville Robbins (U. S. A.)
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Abstract: Let n, r μ/span> N, with r ? 2. Consider the partition functions q0(n), br(n), pr(n), which denote respectively the number of partitions of n into distinct odd parts, parts not divisible by r, parts in r distinct colors. We obtain explicit formulas for each of these partition functions in terms of s(n) (the usual sum-of-divisors function) or s(r)(n) (the sum of the divisors of n that are not multiples of r). |
Keywords and phrases: partitions, divisor sums. |
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