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单词 TableOfPoliteNumberRepresentationsFor1N101
释义

table of polite number representations for 1<n<101


There clearly are patterns to the number of ways to represent a positive integer as a sum of consecutive nonnegative integers. There is only one way to represent odd primes in this manner, whereas composite odd numbersMathworldPlanetmathPlanetmath tend to have more representationsPlanetmathPlanetmath.

To try to make the relationship between integer factorization and number of representations as a sum of consecutive integers, the following table, in additionPlanetmathPlanetmath to listing the different sums and tallying them, also gives the value of the number of (nondistinct) prime factorsMathworldPlanetmath function (http://planetmath.org/NumberOfNondistinctPrimeFactorsFunction) Ω(n) and the differencePlanetmathPlanetmath between the two. But to avoid needless repetition, the sums given are only of positive numbers; the only cases this makes a difference is for the triangular numbersMathworldPlanetmath Tn, which in addition to being representable as

i=1ni

are also representable as

i=0ni.

For sums with more than three addends, the middle addends have been replaced by three dots.

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更新时间:2025/5/4 14:38:54