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Search: id:A061201
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| 1, 4, 7, 13, 16, 25, 28, 38, 44, 53, 56, 74, 77, 86, 95, 110, 113, 131, 134, 152, 161, 170, 173, 203, 209, 218, 228, 246, 249, 276, 279, 300, 309, 318, 327, 363, 366, 375, 384, 414, 417, 444, 447, 465, 483, 492, 495, 540, 546, 564, 573, 591, 594, 624, 633, 663
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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(tau<=)_k(n) = |{(x_1,x_2,...,x_k): x_1*x_2*...*x_k<=n}|, i.e. tau<=_k(n) is number of solutions to x_1*x_2*...*x_k<=n, x_i>0.
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REFERENCES
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M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 239.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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For asymptotics see Huxley.
(tau<=)_k(n)=Sum_{i=1..n} tau_k(i). a(n)=partial sums of A007425.
a(n)=sum(k=1,n,A000005(k)*floor(n/k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 19 2007
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PROGRAM
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(PARI) a(n)=sum(k=1, n, numdiv(k)*floor(n/k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 19 2007
(PARI) { for (n=1, 1000, write("b061201.txt", n, " ", sum(k=1, n, numdiv(k)*(n\k))) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 18 2009]
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CROSSREFS
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Cf. tau_2(n): A000005, tau_3(n): A007425, tau_4(n): A007426, tau_5(n): A061200, tau_6(n): A034695, (unordered) 2-factorizations of n: A038548, (unordered) 3-factorizations of n: A034836, A001055, (tau<=)_2(n): A006218, (tau<=)_4(n): A061202, (tau<=)_5(n): A061203, (tau<=)_6(n): A061204.
Sequence in context: A125758 A151788 A048297 this_sequence A110267 A049698 A074136
Adjacent sequences: A061198 A061199 A061200 this_sequence A061202 A061203 A061204
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 21 2001
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