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Search: id:A063427
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| A063427 |
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a(2) = 2; a(n) = k if n*k/(n+k) is the smallest integer of this form. |
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+0
8
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| 2, 6, 4, 20, 3, 42, 8, 18, 10, 110, 4, 156, 14, 10, 16, 272, 9, 342, 5, 28, 22, 506, 8, 100, 26, 54, 21, 812, 6, 930, 32, 66, 34, 14, 12, 1332, 38, 78, 10, 1640, 7, 1806, 44, 30, 46, 2162, 16, 294, 50, 102, 52, 2756, 27, 66, 8, 114, 58, 3422, 12, 3660, 62, 18, 64, 104
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OFFSET
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2,1
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COMMENT
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Equivalently, smallest c such that 1/n+1/c=1/b has integer solutions.
Largest c is 1/(n(n-1)) since 1/n+1/(n(n-1))=1/(n-1)
Let L(x,y)=x+y be the "basic" linear form. Let Q(x,y)=x^2+x*y+y^2 be the "basic" quadratic form. Let C(x,y)=x^3+y^3+x^2*y+x*y^2+x*y+x^2+y^2+x+y be the "basic" cubic form. Then a(n)=min(x/Q(x,n)=0 mod L(x,n))=min(x/C(x,n)=0 mod L(x,n)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 02 2002
For p=prime, a(p^k) = p^k*(p-1). - Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jan 25 2007
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FORMULA
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a(n) = n*A063428(n)/(n-A063428(n))
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EXAMPLE
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a(6)=3 because 6*3/(6+3)=2 is the smallest integer of the form 6*k/(6+k).
a(10) = 10 since 1/10+1/10 = 1/5, 1/10+1/15 = 1/6, 1/10+1/40 = 1/8, 1/10+1/90 = 1/9, and so the first sum provides the value.
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CROSSREFS
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Cf. A063428.
Sequence in context: A033457 A133936 A065350 this_sequence A066092 A100695 A100140
Adjacent sequences: A063424 A063425 A063426 this_sequence A063428 A063429 A063430
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 19 2001
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EXTENSIONS
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New description from Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 30 2001
Entry revised by njas, Feb 13 2007
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