A072391 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.

1, 3, 5, 9, 11, 16, 18, 23, 28, 33, 35, 44, 46, 51, 56, 64, 66, 76, 78, 87, 92, 97, 99, 111, 118, 123, 129, 138, 140, 154, 156, 165, 170, 175, 180, 198, 200, 205, 210, 222, 224, 238, 240, 249, 259, 264, 266, 283, 292, 304, 309, 318, 320, 333, 338, 350, 355, 360

Offset: 1

Author

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

Keywords

• nonn

Links

• Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, vol. 101, (2002), pp. 105-114.

Crossrefs

Cf. A019554.

Formula

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.

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.