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Presently, I am developing software to search for perfectly partitioned numbers. The partitions of a natural number n is the cardinality of the set of sets of natural numbers whose elements sum to n. This number of paritions is denoted by the partion function, p(n). n said to be perfectly partitioned if it evenly divides p(n).
The goal of this research is to find patterns to assist in the development of theorems regarding perfectly partitioned numbers. The major obstacle in the computation of p(n) is the enormous size of the resultant numbers.
So far, I have identified nine numbers less than 4096 which are perfectly partioned:
p(1) = 1
p(2) = 2
p(3) = 3
p(124) = 2,841,940,500
p(158) = 88,751,778,802
p(342) = 164,637,479,165,761,044
p(693) = 43,397,921,522,754,943,172,592,795
p(1896) = 242,371,131,052,313,431,017,875,037,233,367,567,350,390,976
p(3853) = 52,458,768,232,245,476,848,382,802,651,615,548,511,564,556,404,916,972,885,720,802,646
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