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A359790
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Dirichlet inverse of function f(n) = 1 + n', where n' stands for the arithmetic derivative of n, A003415(n).
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8
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1, -2, -2, -1, -2, 2, -2, -1, -3, 0, -2, 3, -2, -2, -1, 0, -2, 6, -2, 3, -3, -6, -2, 7, -7, -8, -8, 3, -2, 12, -2, 3, -7, -12, -5, 9, -2, -14, -9, 11, -2, 18, -2, 3, 0, -18, -2, 11, -11, 6, -13, 3, -2, 26, -9, 15, -15, -24, -2, 17, -2, -26, -4, 9, -11, 30, -2, 3, -19, 16, -2, 9, -2, -32, 0, 3, -11, 36, -2, 23, -16, -36
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OFFSET
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1,2
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LINKS
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FORMULA
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a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} (1+A003415(n/d)) * a(d).
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PROG
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(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
memoA359790 = Map();
A359790(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359790, n, &v), v, v = -sumdiv(n, d, if(d<n, (1+A003415(n/d))*A359790(d), 0)); mapput(memoA359790, n, v); (v)));
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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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