|
%I #16 Nov 11 2018 10:32:23
%S 1,2,2,3,3,3,5,6,7,7,7,7,7,9,9,10,12,13,13,13,13,13,15,15,16,16,16,18,
%T 18,18,20,21,21,23,23,24,24,24,24,24,26,26,26,26,26,28,30,30,33,34,34,
%U 34,34,34,34,36,36,36,36,36,36,38,40,41,41,41,41,43,43,43,45,46,48,48
%N Partial sums of A035185.
%H M. Baake and R. V. Moody, <a href="http://arXiv.org/abs/math.MG/9904028">Similarity submodules and root systems in four dimensions</a>, Canad. J. Math. 51 (1999), 1258-1276.
%F a(n) = Sum_{k=1..n} A035185(k);
%F a(n) is asymptotic to c*n where c = log(1+sqrt(2))/sqrt(2) = 0.62322524014023051339402008...
%F a(n) = Sum_{k=1..n} K(k,2)*floor(n/k) where K(x,y) is the Kronecker symbol. - _Benoit Cloitre_, Oct 31 2009
%t Table[DivisorSum[n, KroneckerSymbol[2, #]&], {n, 1, 100}] // Accumulate (* _Jean-François Alcover_, Nov 11 2018 *)
%o (PARI) a(n)=sum(k=1,n,kronecker(k,2)*floor(n/k)) \\ _Benoit Cloitre_, Oct 31 2009
%Y Cf. A035185, A078428.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Dec 31 2002
%E Corrected by _T. D. Noe_, Nov 02 2006
|
