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Search: id:A005279
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| A005279 |
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Numbers having divisors d,e with d < e < 2d.
(Formerly M4093)
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+0
9
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| 6, 12, 15, 18, 20, 24, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 75, 77, 78, 80, 84, 88, 90, 91, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 140, 143, 144, 150, 153, 154, 156, 160, 162, 165, 168, 170, 174, 175, 176
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Arithmetic and harmonic means of A046793(n) and a(n) both integers.
n is in this sequence iff n is a multiple of some term in A020886.
a(n) is also a positive integer v for which there exists a smaller positive integer u such that the contraharmonic mean (uu+vv)/(u+v) is an integer c (in fact, there are two distinct values u giving with v the same c). [From Pahikkala Jussi (pahio(AT)wakkanet.fi), Dec 14 2008]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. K. Guy, Unsolved Problems in Number Theory, E3.
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LINKS
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Planet Math., Proposition 4
Planet Math., Definition
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MAPLE
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isA005279 := proc(n) local divs, d, e ; divs := numtheory[divisors](n) ; for d from 1 to nops(divs)-1 do for e from d+1 to nops(divs) do if divs[e] < 2*divs[d] then RETURN(true) ; fi ; od: od: RETURN(false) : end; for n from 3 to 300 do if isA005279(n) then printf("%d, ", n) ; fi ; od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
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CROSSREFS
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Cf. A010814.
Sequence in context: A114304 A107487 A092671 this_sequence A129512 A116359 A141698
Adjacent sequences: A005276 A005277 A005278 this_sequence A005280 A005281 A005282
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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