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Search: id:A072391
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| A072391 |
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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. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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LINKS
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Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, vol. 101, (2002), pp. 105-114.
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FORMULA
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a(n)=Sum_{k<=n} (floor(n/A019554(k))) Asymptotic expression: a(n)=(n*ln(n)^2/(4*zeta(2)))+(n*ln(n)/zeta(2))*((3*gamma/2)-(zeta'(2)/zeta(2))), gamma = A001620.
Asymptotic expression (includes error term): a(n)=(n*ln(n)^2/(4*zeta(2)))+(n*ln(n)/zeta(2))*((3*gamma/2)-(zeta'(2)/zeta(2)))+O(n), gamma = A001620.
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CROSSREFS
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Cf. A019554.
Sequence in context: A024903 A018486 A024414 this_sequence A036696 A111039 A114512
Adjacent sequences: A072388 A072389 A072390 this_sequence A072392 A072393 A072394
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KEYWORD
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nonn
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AUTHOR
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Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002
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