

A007410


Numerator of Sum k^(4); k = 1..n.
(Formerly M5050)


34



1, 17, 1393, 22369, 14001361, 14011361, 33654237761, 538589354801, 43631884298881, 43635917056897, 638913789210188977, 638942263173398977, 18249420414596570742097, 18249859383918836502097, 18250192489014819937873
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OFFSET

1,2


COMMENTS

p divides a(p1) for prime p>5. p divides a((p1)/2) for prime p>5. p^2 divides a((p1)/2) for prime p=31,37.  Alexander Adamchuk, Jul 07 2006
p^2 divides a(p1) 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. 1220 of E. Kaltofen and S. M. Watt, editors, Computers and Mathematics, SpringerVerlag, 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



