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Search: id:A128700
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| A128700 |
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Highly abundant numbers with an odd divisor sum. |
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4
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| 1, 2, 4, 8, 16, 18, 36, 72, 144, 288, 1800, 3600, 7200
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Alaoglu and Erdos showed that 7200 is the largest highly abundant number with all the exponents of its prime factors occurring to powers greater than unity. It follows that the sequence of highly abundant numbers with an odd divisor sum is finite, and is bounded above by 7200. Accordingly, this is the complete sequence of such integers.
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REFERENCES
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Alaoglu, L., Erdos, P.; On Highly Composite and Similar Numbers, Transactions of the American Mathematical Society, Vol. 56, No. 3, (November 1944), pp. 448-469.
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LINKS
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Wikepedia, Highly Abundant Numbers.
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FORMULA
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The highly abundant numbers are those integers for which sigma(n) > sigma(m) for all m < n (A002093). This sequence contains those elements of A002093 that have an odd divisor sum.
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EXAMPLE
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The fifth highly abundant number with an odd divisor sum is 15. Hence a(5)=15
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MATHEMATICA
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hadata1=FoldList[Max, 1, Table[DivisorSigma[1, n], {n, 2, 7200}]]; data1=Flatten[Position[hadata1, #, 1, 1]&/@Union[hadata1]]; Select[data1, OddQ[DivisorSigma[1, # ]] &]
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CROSSREFS
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Cf. A002093, A000203.
Sequence in context: A088827 A076057 A133809 this_sequence A018547 A018383 A051513
Adjacent sequences: A128697 A128698 A128699 this_sequence A128701 A128702 A128703
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KEYWORD
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easy,full,nice,nonn,fini
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Mar 28 2007
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