A349347 Sum of A181988 and its Dirichlet inverse, where A181988(n) = A001511(n)*A003602(n).

2, 0, 0, 4, 0, 8, 0, 4, 4, 12, 0, 4, 0, 16, 12, 5, 0, 12, 0, 6, 16, 24, 0, 8, 9, 28, 12, 8, 0, 8, 0, 6, 24, 36, 24, 14, 0, 40, 28, 12, 0, 12, 0, 12, 26, 48, 0, 10, 16, 34, 36, 14, 0, 32, 36, 16, 40, 60, 0, 28, 0, 64, 36, 7, 42, 20, 0, 18, 48, 24, 0, 20, 0, 76, 46, 20, 48, 24, 0, 15, 37, 84, 0, 38, 54, 88, 60, 24, 0, 40

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = A181988(n) + A349346(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A181988(d) * A349346(n/d).

Prog

(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];
A349347(n) = (A181988(n)+A349346(n));

Crossrefs

Cf. A001511, A003602, A181988, A349346.

Sequence in context: A140668 A353369 A323900 * A354187 A349345 A349357

Adjacent sequences: A349344 A349345 A349346 * A349348 A349349 A349350

Keyword

nonn

Author

Antti Karttunen, Nov 15 2021

Status

approved