A072391 - OEIS

%I #5 Jul 11 2015 17:32:13

%S 1,3,5,9,11,16,18,23,28,33,35,44,46,51,56,64,66,76,78,87,92,97,99,111,

%T 118,123,129,138,140,154,156,165,170,175,180,198,200,205,210,222,224,

%U 238,240,249,259,264,266,283,292,304,309,318,320,333,338,350,355,360

%N D2(n,n) = Sum_{1<=k<=n} (d_n(k^2)), where d_a(k^2)=card{d: d|k and 1<=d<=a} for real a.

%H Kevin A. Broughan, <a href="http://www.math.waikato.ac.nz/~kab/papers/div4.pdf">Restricted divisor sums</a>, Acta Arithmetica, vol. 101, (2002), pp. 105-114.

%F a(n)=Sum_{k<=n} (floor(n/A019554(k))) Asymptotic expression: a(n)=(n*log(n)^2/(4*zeta(2)))+(n*log(n)/zeta(2))*((3*gamma/2)-(zeta'(2)/zeta(2))), gamma = A001620.

%F Asymptotic expression (includes error term): a(n)=(n*log(n)^2/(4*zeta(2)))+(n*log(n)/zeta(2))*((3*gamma/2)-(zeta'(2)/zeta(2)))+O(n), gamma = A001620.

%Y Cf. A019554.

%K nonn

%O 1,2

%A Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002