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A078462
Partial sums of A035185.
1
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
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
Sequence in context: A240519 A318037 A326165 * A239518 A293924 A307730
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Dec 31 2002
EXTENSIONS
Corrected by T. D. Noe, Nov 02 2006
STATUS
approved