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A305807
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Dirichlet inverse of A032742 (the largest proper divisor of n).
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4
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1, -1, -1, -1, -1, -1, -1, -1, -2, -3, -1, 1, -1, -5, -3, -1, -1, 0, -1, 1, -5, -9, -1, 3, -4, -11, -4, 1, -1, 5, -1, -1, -9, -15, -5, 6, -1, -17, -11, 5, -1, 7, -1, 1, -2, -21, -1, 5, -6, -8, -15, 1, -1, 4, -9, 7, -17, -27, -1, 19, -1, -29, -4, -1, -11, 11, -1, 1, -21, -3, -1, 8, -1, -35, -8, 1, -9, 13, -1, 9, -8, -39, -1, 29, -15, -41, -27, 11, -1
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OFFSET
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1,9
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LINKS
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FORMULA
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a(1) = 1; for n > 1, a(n) = -Sum_{d|n, d<n} A032742(n/d)*a(d).
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MATHEMATICA
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b[n_] := If[n == 1, 1, Divisors[n][[-2]]];
a[n_] := a[n] = If[n == 1, 1, -Sum[b[n/d] a[d], {d, Most@ Divisors[n]}]];
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PROG
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(PARI)
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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