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A064169
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Numerator - denominator in n-th harmonic number, 1 + 1/2 + 1/3 +...+ 1/n.
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2
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0, 1, 5, 13, 77, 29, 223, 481, 4609, 4861, 55991, 58301, 785633, 811373, 835397, 1715839, 29889983, 10190221, 197698279, 40315631, 13684885, 13920029, 325333835, 990874363, 25128807667, 25472027467, 232222818803, 235091155703, 6897956948587, 6975593267347
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The numerator and denominator in the definition have no common factors >1.
Numerator of ( HarmonicNumber[n] - 1 ). - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 09 2006
p divides a(p-2) for prime p>3. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 09 2006
It appears that a(n) = numerator((3*(HarmonicNumber(n)-1)) / (n*(n^2+6*n+11)), except for n = 5, 82, 115, and 383 (tested to 20,000). [From Gary Detlefs, Jul 20 2011]
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics - Harmonic Number.
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FORMULA
| Numerators of gamma+Psi(n+1)-1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 12 2002
a(n) = Numerator[ Sum[ 1/k, {k,2,n} ]]. a(n) = A001008(n) - A002805(n). a(n) = Numerator[ HarmonicNumber[n] - 1 ] a(n) = Numerator[ A001008(n)/A002805(n) -1 ] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 09 2006
a(n)= Numerator of A027612(n-1)/(A027611(n)*n^2*(n-1)!),n>1. [From Gary Detlefs, Aug 05 2011]
a(n)= Numerator(sum(1/(3*k+3),k=1..n-1))[From Gary Detlefs, Sep 14 2011]
a(n)= Numerator(sum(2/(k+2),k=0..n-1))[From Gary Detlefs, Oct 06 2011]
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EXAMPLE
| The 3rd harmonic number is 11/6. So a(3) = 11 - 6 = 5.
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MAPLE
| ZL:=n->sum(1/i, i=2..n): a:=n->floor(numer(ZL(n))): seq(a(n), n=1..28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2007
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MATHEMATICA
| f[ n_ ] := (s = Sum[ 1/k, {k, 1, n} ]; Numerator[ s ] - Denominator[ s ]); Table[ f[ n ], {n, 1, 25} ]
Numerator[Table[Sum[1/k, {k, 2, n}], {n, 1, 30}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 09 2006
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CROSSREFS
| Cf. A001008, A002805.
Sequence in context: A137702 A140120 A163732 * A081525 A027612 A027457
Adjacent sequences: A064166 A064167 A064168 * A064170 A064171 A064172
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Sep 19 2001
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EXTENSIONS
| One more term from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 28 2001
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 12 2002
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