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Antti Karttunen, <a href="/A349346/b349346.txt">Table of n, a(n) for n = 1..20000</a>

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Cf. also A347957, A349134, A349344.

Cf. also A349134, A349344.

allocatedDirichlet inverse forof AnttiA181988, where KarttunenA181988(n) = A001511(n)*A003602(n).

1, -2, -2, 1, -3, 4, -4, 0, -1, 6, -6, -2, -7, 8, 4, 0, -9, 2, -10, -3, 5, 12, -12, 0, -4, 14, -2, -4, -15, -8, -16, 0, 7, 18, 6, -1, -19, 20, 8, 0, -21, -10, -22, -6, 3, 24, -24, 0, -9, 8, 10, -7, -27, 4, 8, 0, 11, 30, -30, 4, -31, 32, 4, 0, 9, -14, -34, -9, 13, -12, -36, 0, -37, 38, 8, -10, 9, -16, -40, 0, -4, 42

1,2

a(1) = 1; a(n) = -Sum_{d|n, d < n} A181988(n/d) * a(d).

a(n) = A349347(n) - A181988(n).

(PARI)

up_to = 20000;

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.

A001511(n) = 1+valuation(n, 2);

A003602(n) = (1+(n>>valuation(n, 2)))/2;

A181988(n) = (A001511(n)*A003602(n));

v349346 = DirInverseCorrect(vector(up_to, n, A181988(n)));

A349346(n) = v349346[n];

Cf. A001511, A003602, A181988, A349347.

Cf. also A349344.

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Antti Karttunen, Nov 15 2021

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