A007409 Denominators of Sum_{k=1..n} 1/k^3.

1, 8, 216, 1728, 216000, 24000, 8232000, 65856000, 16003008000, 16003008000, 21300003648000, 21300003648000, 46796108014656000, 46796108014656000, 46796108014656000, 374368864117248000, 1839274229408039424000

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• easy
• frac

Comments

Largest prime factor in A007409(n) (n > 1) is A007917(n), occurring always to the power 3. - M. F. Hasler, Nov 10 2006

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

Crossrefs

Cf. A007408, A007917.

Programs

Maple

A007409:= n->denom(sum(1/k^3,k=1..n)); # M. F. Hasler, Nov 10 2006

Mathematica

Table[Denominator[Sum[1/k^3, {k, n}]], {n, 10}] (* Alonso del Arte, Dec 30 2012 *)