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Search: id:A100832
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| A100832 |
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Amenable numbers: n such that there exists a multiset of integers (s(1), ..., s(n)) whose size, sum and product are all n. |
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+0
1
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| 1, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, 60, 61, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 96, 97, 100, 101, 104, 105, 108, 109, 112, 113, 116, 117, 120, 121, 124, 125, 128, 129, 132
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Essentially the same as A042948.
The set {s(i)} is closed under multiplication. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 21 2005
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REFERENCES
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O. P. Lossers, Solution to problem 10454, "Amenable Numbers", Amer. Math. Monthly Vol. 105 No. 4 April 1998 MAA Washington DC.
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LINKS
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Eric Weisstein's World of Mathematics, Amenable Number
Wikipedia, Amenable number
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FORMULA
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Consists of the numbers n == 0 or 1 (mod 4), excluding n=4.
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EXAMPLE
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5 and 8, for instance, are in the sequence because we have 5=1-1+1-1+5=1*(-1)*1*(-1)*5 and 8=1-1+1-1+1+1+2+4=1*(-1)*1*(-1)*1*1*2*4.
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CROSSREFS
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Cf. A014601.
Sequence in context: A165991 A101079 A066812 this_sequence A034812 A066467 A072833
Adjacent sequences: A100829 A100830 A100831 this_sequence A100833 A100834 A100835
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 07 2005
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jan 24 2005
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