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

1,2

Links

Table of n, a(n) for n=1..74.

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A035185, A078428.

Sequence in context: A240519 A318037 A326165 * A239518 A293924 A307730

Adjacent sequences: A078459 A078460 A078461 * A078463 A078464 A078465

Keyword

nonn

Author

Benoit Cloitre, Dec 31 2002

Extensions

Corrected by T. D. Noe, Nov 02 2006

Status

approved