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A007410 Numerator of Sum k^(-4); k = 1..n.
(Formerly M5050)
33
1, 17, 1393, 22369, 14001361, 14011361, 33654237761, 538589354801, 43631884298881, 43635917056897, 638913789210188977, 638942263173398977, 18249420414596570742097, 18249859383918836502097, 18250192489014819937873 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

p divides a(p-1) for prime p>5. p divides a((p-1)/2) for prime p>5. p^2 divides a((p-1)/2) for prime p=31,37. - Alexander Adamchuk, Jul 07 2006

p^2 divides a(p-1) for prime p = 37. - Alexander Adamchuk, Nov 07 2006

Denominators are A007480. See the W. Lang link under A103345 for the rationals and more.

The limit of the rationals Zeta(n):=Sum[1/k^4,{k,1,n}] for n->infinity is (Pi^4)/90 which is approximately 1.082323234.

REFERENCES

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.

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

LINKS

T. D. Noe, Table of n, a(n) for n=1..200

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

FORMULA

Numerators of coefficients in expansion of PolyLog(4, x)/(1 - x). - Ilya Gutkovskiy, Apr 10 2017

MATHEMATICA

Numerator[Table[Sum[1/k^4, {k, 1, n}], {n, 1, 20}]] - Alexander Adamchuk, Jul 07 2006

PROG

(PARI) a(n)=numerator(sum(k=1, n, 1/k^4)) \\ Charles R Greathouse IV, Jul 19 2011

CROSSREFS

Cf. A001008, A007406, A007408, A007480.

Sequence in context: A067409 A219562 A183236 * A203229 A269791 A256020

Adjacent sequences:  A007407 A007408 A007409 * A007411 A007412 A007413

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.