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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
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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
| Eric Weisstein's World of Mathematics, Amenable Number
Wikipedia, Amenable number
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FORMULA
| Consists of the numbers n == 0 or 1 (mod 4), excluding n=4.
a(n)=a(n-1)+a(n-2)-a(n-3), n>4. G.f.: x*(1+3*x)*(1+x-x^2)/(1-x-x^2+x^3). [Colin Barker, Jan 26 2012]
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EXAMPLE
| 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
| Cf. A014601.
Sequence in context: A191977 A101079 A066812 * A034812 A066467 A180244
Adjacent sequences: A100829 A100830 A100831 * A100833 A100834 A100835
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 07 2005
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jan 24 2005
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