The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 FORMULA From G. C. Greubel, Jul 24 2023: (Start) a(n) = 2*A117664(n). a(n) = 2*A111876(n-1)/n. (End) EXAMPLE The first few fractions are 1/2, 7/6, 37/20, 533/210, 1627/504, 18107/4620, 237371/51480, ... = A117731/a(n). 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 (Magma) [Denominator(n*(HarmonicNumber(2*n) -HarmonicNumber(n))): n in [1..40]]; // G. C. Greubel, Jul 24 2023 (SageMath) [denominator(n*(harmonic_number(2*n, 1) - harmonic_number(n, 1))) for n in range(1, 41)] # G. C. Greubel, Jul 24 2023 CROSSREFS Cf. A111876, A117731 (numerators), A117664. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 15:47 EDT 2024. Contains 375056 sequences. (Running on oeis4.)