The On-Line Encyclopedia of Integer Sequences (OEIS)

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A111921

Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^4)).
(history; published version)

#10 by Charles R Greathouse IV at Sun Feb 16 08:32:58 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/OddPart.html">Odd Part</a>

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/AperysConstant.html">Apery's constant</a>

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#9 by Susanna Cuyler at Wed Dec 25 08:34:34 EST 2019

STATUS

proposed

approved

#8 by Michel Marcus at Wed Dec 25 02:15:24 EST 2019

STATUS

editing

proposed

#7 by Michel Marcus at Wed Dec 25 02:15:21 EST 2019

CROSSREFS

Cf. A000265, A002117, A111930, A111919, A111920, A111923.

STATUS

proposed

editing

#6 by Jon E. Schoenfield at Wed Dec 25 00:21:07 EST 2019

STATUS

editing

proposed

#5 by Jon E. Schoenfield at Wed Dec 25 00:21:05 EST 2019

NAME

Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^4): 1<=k<=n).

REFERENCES

G. Polya Pólya and G. Szego, Szegő, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50.

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:50:53 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Aug 21 2005

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#3 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,frac,new

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Aug 21 2005

#2 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

COMMENTS

x(n) = A111920(n)/a(n) ---> 14*zeta(3)/15.

REFERENCES

G. Polya and G. Szego, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, sectSect. 6, Problem 50.

KEYWORD

nonn,frac,new

#1 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

NAME

Denominator of x(n) = Sum((odd part of k)/(k^4): 1<=k<=n).

DATA

1, 16, 432, 6912, 864000, 864000, 296352000, 4741632000, 128024064000, 128024064000, 170400029184000, 170400029184000, 374368864117248000, 374368864117248000, 14974754564689920, 239596073035038720

OFFSET

1,2

COMMENTS

Numerator of x(n) = A111920(n);

x(n) = A111920(n)/a(n) ---> 14*zeta(3)/15.

REFERENCES

G. Polya and G. Szego, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, sect. 6, Problem 50.

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddPart.html">Odd Part</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AperysConstant.html">Apery's constant</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

CROSSREFS

Cf. A000265, A002117, A111930, A111919, A111923.

KEYWORD

nonn,frac

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 21 2005

STATUS

approved