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2, 0, 0, 1, 0, 4, 0, 9, 4, 4, 0, 32, 0, 8, 8, 49, 0, 56, 0, 36, 16, 4, 0, 153, 4, 8, 56, 66, 0, 96, 0, 207, 8, 4, 16, 295, 0, 8, 16, 187, 0, 168, 0, 48, 120, 12, 0, 553, 16, 80, 8, 78, 0, 444, 8, 323, 16, 4, 0, 480, 0, 12, 216, 745, 16, 144, 0, 60, 24, 200, 0, 1016, 0, 8, 152, 90, 16, 216, 0, 723, 472, 4, 0, 786, 8, 8, 8, 289
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OFFSET
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1,1
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COMMENTS
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Sum of {the pointwise sum of A336853 and A063524 (1, 0, 0, 0, ...)} and its Dirichlet inverse.
The first negative term is a(720) = -6306.
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LINKS
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FORMULA
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a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A336853(d) * A347098(n/d).
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PROG
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(PARI)
up_to = 16384;
A336853(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)-n); };
Aux347098(n) = if(1==n, n, A336853(n));
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
v347098 = DirInverseCorrect(vector(up_to, n, Aux347098(n)));
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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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