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 A064169 Numerator - denominator in n-th harmonic number, 1 + 1/2 + 1/3 +...+ 1/n. 4
 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; text; internal format)
 OFFSET 1,3 COMMENTS The numerator and denominator in the definition have no common factors > 1. Numerator of ( HarmonicNumber[n] - 1 ). - Alexander Adamchuk, Jun 09 2006 p divides a(p-2) for prime p > 3. - Alexander Adamchuk, 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). - Gary Detlefs, Jul 20 2011 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Harmonic Number FORMULA Numerators of gamma+Psi(n+1)-1. - Vladeta Jovovic, Aug 12 2002 From Alexander Adamchuk, Jun 09 2006: (Start) a(n) = numerator(Sum_{k=2..n} 1/k). a(n) = A001008(n) - A002805(n). a(n) = numerator(HarmonicNumber(n) - 1). a(n) = numerator(A001008(n)/A002805(n) - 1). (End) a(n) = numerator of A027612(n-1)/(A027611(n)*n^2*(n-1)!), n > 1. - Gary Detlefs, Aug 05 2011 a(n) = numerator(Sum_{k=1..n-1} 1/(3*k + 3)). - Gary Detlefs, Sep 14 2011 a(n) = numerator(Sum_{k=0..n-1} 2/(k+2)). - Gary Detlefs, Oct 06 2011 EXAMPLE The 3rd harmonic number is 11/6. So a(3) = 11 - 6 = 5. MAPLE ZL:=n->sum(1/i, i=2..n): a:=n->floor(numer(ZL(n))): seq(a(n), n=1..28); # Zerinvary Lajos, Mar 28 2007 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, Jun 09 2006 *) Numerator[#]-Denominator[#]&/@HarmonicNumber[Range[30]] (* Harvey P. Dale, Apr 25 2016 *) CROSSREFS Cf. A001008, A002805. Sequence in context: A163732 A208821 A293259 * A294208 A081525 A027612 Adjacent sequences:  A064166 A064167 A064168 * A064170 A064171 A064172 KEYWORD nonn AUTHOR Leroy Quet, Sep 19 2001 EXTENSIONS One more term from Robert G. Wilson v, Sep 28 2001 More terms from Vladeta Jovovic, Aug 12 2002 STATUS approved

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