A353336 Sum of A353420 and its Dirichlet inverse.

2, 0, 0, 1, 0, 4, 0, 1, 4, 6, 0, 2, 0, 8, 12, 1, 0, 14, 0, 3, 16, 10, 0, 2, 9, 12, 28, 4, 0, 12, 0, 1, 20, 14, 24, 9, 0, 16, 24, 3, 0, 22, 0, 5, 66, 20, 0, 2, 16, 25, 28, 6, 0, 56, 30, 4, 32, 22, 0, 12, 0, 26, 100, 1, 36, 24, 0, 7, 40, 28, 0, 9, 0, 28, 86, 8, 40, 34, 0, 3, 157, 30, 0, 19, 42, 32, 44, 5, 0, 52, 48

Offset

1,1

Comments

The first negative term is a(255255) = -11936.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A353420(n) + A353335(n).

For n > 1, a(n) = -Sum_{d|n, 1<d<n} A353420(d) * A353335(n/d).

Prog

(PARI)
up_to = 65537;
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 (correctly!)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
A353420(n) = A126760(A003961(n));
v353335 = DirInverseCorrect(vector(up_to, n, A353420(n)));
A353335(n) = v353335[n];
A353336(n) = (A353420(n)+A353335(n));

Crossrefs

Cf. A003961, A126760, A353420 (also a quadrisection of this sequence), A353335.

Cf. also A323882, A323894, A349135.

Sequence in context: A346236 A323365 A349135 * A349126 A340188 A323911

Adjacent sequences: A353333 A353334 A353335 * A353337 A353338 A353339

Keyword

sign

Author

Antti Karttunen, Apr 20 2022

Status

approved