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A051470
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a(n) is least value of m for which the sum of Liouville's function from 1 to m is n.
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12
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1, 906150258, 906150259, 906150260, 906150263, 906150264, 906150331, 906150334, 906150337, 906150338, 906150339, 906150358, 906150359, 906150362, 906150363, 906150368, 906150387, 906150388, 906150389, 906150406, 906150407
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OFFSET
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1,2
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COMMENTS
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It was once conjectured that the sum of Liouville's function was never > 0 except for the first term.
It follows from Theorem 2 in Borwein-Ferguson-Mossinghoff that a(n) < 262*n^2 infinitely often, improving on an earlier result of Anderson & Stark. - Charles R Greathouse IV, Jun 14 2011
a(830) > 2 * 10^14 (probably around 3.511e14) and a(1160327) = 351753358289465 according to the calculations of Borwein, Ferguson, & Mossinghoff. - Charles R Greathouse IV, Jun 14 2011
a(n) is the smallest m such that A002819(m) = n.
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REFERENCES
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R. J. Anderson and H. M. Stark, Oscillation theorems, Analytic Number Theory (1980); Lecture Notes in Mathematics 899 (1981), pp. 79-106.
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LINKS
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EXAMPLE
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The sum of Liouville's function from 1 through 906150258 is 2, that is the smallest value, so a(2)=906150258.
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PROG
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(PARI) print1(r=1); t=0; for(n=906150257, 906400000, t+=(-1)^bigomega(n); if(t>r, r=t; print1(", "n))) \\ Charles R Greathouse IV, Jun 14 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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