1,2

By Theorem 131 in Hardy and Wright, p^2 divides a(p-1) for prime p > 5. - T. D. Noe (noe(AT)sspectra.com), Sep 05 2002

p^3 divides a(p-1) for prime p = 37. Primes p such that p divides a((p+1)/2) are listed in A124787(n) = {3, 11, 17, 89}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 07 2006

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

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford Univ. Press, 1971, page 104.

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.

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

Sum[1/k^3, {k, 1, n}] = Sqrt[Sum[Sum[1/(i*j)^3, {i, 1, n}], {j, 1, n}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 26 2004

A007408:=n->numer(sum(1/k^3, k=1..n)); map(%, [$1..20]); - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 10 2006

s=0; lst={}; Do[s+=n^1/n^4; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 24 2009]

Cf. A001008, A007406, A007409.

Cf. A124787.

Sequence in context: A012202 A012098 A012072 this_sequence A066989 A160501 A075987

Adjacent sequences: A007405 A007406 A007407 this_sequence A007409 A007410 A007411

nonn,frac

N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein