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A007407 a(n) = denominator of Sum_{k=1..n} 1/k^2.
(Formerly M3661)
46
1, 4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 1270080, 153679680, 153679680, 25971865920, 25971865920, 129859329600, 519437318400, 150117385017600, 150117385017600, 54192375991353600, 10838475198270720, 221193371393280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1152 (terms 1..200 from T. D. Noe)

D. Y. Savio, E. A. Lamagna and S.-M. Liu, Summation of harmonic numbers, pp. 12-20 of E. Kaltofen and S. M. Watt, editors, Computers and Mathematics, Springer-Verlag, NY, 1989.

FORMULA

a(n) = denominator of (Pi^2)/6 - zeta(2, x). - Artur Jasinski, Mar 03 2010

a(n) = A001044(n) / gcd(A001819(n), A001044(n)). - Daniel Suteu, Dec 25 2016

EXAMPLE

1/1^2 + 1/2^2 + 1/3^2 = 1/1 + 1/4 + 1/9 = 49/36, so a(3) = 36. - Jon E. Schoenfield, Dec 26 2014

MAPLE

ZL:=n->sum(1/i^2, i=2..n): a:=n->floor(denom(ZL(n))): seq(a(n), n=1..21); # Zerinvary Lajos, Mar 28 2007

MATHEMATICA

s=0; lst={}; Do[s+=n^2/n^4; AppendTo[lst, Denominator[s]], {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 24 2009 *)

Table[Denominator[Pi^2/6 - Zeta[2, x]], {x, 1, 22}] (* Artur Jasinski, Mar 03 2010 *)

Denominator[Accumulate[1/Range[30]^2]] (* Harvey P. Dale, Nov 08 2012 *)

PROG

(Haskell)

import Data.Ratio ((%), denominator)

a007407 n = a007407_list !! (n-1)

a007407_list = map denominator $

                   scanl1 (+) $ map (1 %) $ tail a000290_list

-- Reinhard Zumkeller, Jul 06 2012

(PARI) a(n)=denominator(sum(k=1, n, 1/k^2)) \\ Charles R Greathouse IV, Nov 20 2012

(Python)

from fractions import Fraction

def A007407(n): return sum(Fraction(1, k**2) for k in range(1, n+1)).denominator # Chai Wah Wu, Apr 03 2021

CROSSREFS

Cf. A007406 (numerators), A000290, A035166.

Sequence in context: A334580 A068589 A120077 * A051418 A069046 A065886

Adjacent sequences:  A007404 A007405 A007406 * A007408 A007409 A007410

KEYWORD

nonn,easy,frac,nice,changed

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified April 15 20:35 EDT 2021. Contains 342977 sequences. (Running on oeis4.)