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A193758 Denominator of H(n)/H(n-1), where H(n) is the n-th harmonic number = Sum_{k=1..n} 1/k. 2
2, 9, 22, 125, 137, 343, 726, 6849, 7129, 81191, 83711, 1118273, 1145993, 1171733, 2391514, 41421503, 42142223, 271211719, 275295799, 55835135, 18858053, 439143531, 1332950097, 33695573875, 34052522467, 309561680403, 312536252003, 9146733078187 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) mod n^3 = 0 iff n is prime > 3. - Gary Detlefs, Jan 30 2013

LINKS

Table of n, a(n) for n=2..29.

FORMULA

a(n) = denominator(H(n)/H(n-1)), where H(n) = Sum_{k=1..n} 1/k.

a(n) = numerator(n*H(n))-denominator(n*H(n)). - Gary Detlefs, Sep 05 2011

MAPLE

H:= n-> add(1/k, k=1..n): seq(denom(H(n)/H(n-1)), n=2..25);

MATHEMATICA

h[n_] := Sum[1/i, {i, n}]; Table[Denominator[h[n]/h[n - 1]], {n, 2, 50}] (* T. D. Noe, Aug 04 2011 *)

Denominator[#[[2]]/#[[1]]]&/@Partition[HarmonicNumber[Range[30]], 2, 1] (* Harvey P. Dale, Jul 05 2015 *)

CROSSREFS

Cf. A001008, A002805.

Sequence in context: A032315 A032224 A254710 * A082940 A032149 A032054

Adjacent sequences:  A193755 A193756 A193757 * A193759 A193760 A193761

KEYWORD

nonn

AUTHOR

Gary Detlefs, Aug 04 2011

STATUS

approved

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Last modified February 23 18:54 EST 2019. Contains 320438 sequences. (Running on oeis4.)