A078462 Partial sums of A035185.

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, 18, 18, 20, 21, 21, 23, 23, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26, 28, 30, 30, 33, 34, 34, 34, 34, 34, 34, 36, 36, 36, 36, 36, 36, 38, 40, 41, 41, 41, 41, 43, 43, 43, 45, 46, 48, 48

Offset: 1

Author

Benoit Cloitre, Dec 31 2002

Keywords

• nonn

Links

• M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, Canad. J. Math. 51 (1999), 1258-1276.

Crossrefs

Cf. A035185, A078428.

Programs

Mathematica

Table[DivisorSum[n, KroneckerSymbol[2, #]&], {n, 1, 100}] // Accumulate (* Jean-François Alcover, Nov 11 2018 *)

PARI

a(n)=sum(k=1,n,kronecker(k,2)*floor(n/k)) \\ Benoit Cloitre, Oct 31 2009

Formula

a(n) = Sum_{k=1..n} A035185(k);

a(n) is asymptotic to c*n where c = log(1+sqrt(2))/sqrt(2) = 0.62322524014023051339402008...

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

Extensions

Corrected by T. D. Noe, Nov 02 2006