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A296519 Denominator of n*Sum_{k=1..n} 1/(n+k). 2
2, 6, 20, 210, 504, 4620, 51480, 18018, 272272, 23279256, 21162960, 446185740, 2059318800, 5736673800, 22181805360, 1289317436550, 1213475234400, 8022419605200, 281206918792800, 267146572853160, 10431437606647200, 428163098127382800, 409547311252279200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is divisible by all primes p such that the numerator of Sum_{n < k*p <= n} 1/k is not divisible by p, in particular by all primes from n+1 to 2*n-1. - Robert Israel, May 21 2020

LINKS

Robert Israel, Table of n, a(n) for n = 1..1155

EXAMPLE

The first few fractions are 1/2, 7/6, 37/20, 533/210, 1627/504, 18107/4620, 237371/51480, ... = A117731/A296519.

MAPLE

N:= 30: # for a(1)..a(N)

H:= ListTools:-PartialSums([seq(1/i, i=1..2*N)]):

map(n -> denom(n*(H[2*n]-H[n])), [$1..N]); # Robert Israel, May 21 2020

MATHEMATICA

Table[n (HarmonicNumber[2 n] - HarmonicNumber[n]), {n, 30}] // Denominator

PROG

(PARI) a(n) = denominator(n*sum(k=1, n, 1/(n+k))); \\ Michel Marcus, Dec 14 2017

CROSSREFS

Cf. A117731 (numerators).

Sequence in context: A274714 A074008 A156334 * A082690 A104861 A074859

Adjacent sequences:  A296516 A296517 A296518 * A296520 A296521 A296522

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Dec 14 2017

STATUS

approved

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Last modified April 18 14:46 EDT 2021. Contains 343089 sequences. (Running on oeis4.)