1,2

By Wolstenholme's theorem, p divides a(p-1) for prime p > 3. - T. D. Noe (noe(AT)sspectra.com), Sep 05 2002

Also p divides a( (p-1)/2 ) for prime p > 3. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 07 2006

The rationals a(n)/A007407(n) converge to Zeta(2)= (Pi^2)/6 = 1.6449340668... (see the decimal expansion A013661).

For the rationals a(n)/A007407(n), n>=1, see the W. Lang link under A103345 (case k=2).

Numbers n such that a(n) is prime are listed in A111354[n] = {2,7,13,19,121,188,252,368,605,745,1085,1127,1406,...}. Primes in a(n) are listed in A123751[n] = {5,266681,40799043101,86364397717734821,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 11 2006

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

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

Hisanori Mishima, Factorizations of many number sequences

Eric Weisstein's World of Mathematics, Wolstenholme's Theorem

Eric Weisstein's World of Mathematics, Wolstenholme Number

Sum[1/k^2, {k, 1, n}] = Sqrt[Sum[Sum[1/(i*j)^2, {i, 1, n}], {j, 1, n}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 26 2004

G.f. for rationals a(n)/A007407(n), n>=1: polylog(2,x)/(1-x).

ZL:=n->sum(1/i^2, i=1..n): a:=n->floor(numer(ZL(n))): seq(a(n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2007

s=0; lst={}; Do[s+=n^2/n^4; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 24 2009]

Cf. A001008, A007407.

Cf. A111354, A123751.

Sequence in context: A108207 A127091 A063429 this_sequence A058927 A083224 A093188

Adjacent sequences: A007403 A007404 A007405 this_sequence A007407 A007408 A007409

nonn,frac,easy,nice

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