A072391 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..58.

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

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.

CROSSREFS

Cf. A019554.

Sequence in context: A018486 A261194 A024414 * A310038 A372051 A036696

Adjacent sequences: A072388 A072389 A072390 * A072392 A072393 A072394

KEYWORD

nonn

AUTHOR

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

STATUS

approved