A342417 Dirichlet inverse of Čiurlionis sequence, A342002.

1, -1, -5, -1, -7, 9, -7, -5, -6, 1, -41, 5, -9, 3, 33, -1, -47, -6, -11, 19, 27, 63, -53, 41, 36, 1, 136, 7, -59, 7, -9, 25, 369, 77, 43, 16, -59, -49, -157, -9, -317, -19, -73, -13, -10, -21, -359, -53, -38, -52, 139, -105, -401, -348, 473, -23, -263, -51, -443, -201, -11, 5, 292, 23, 65, -893, -69, -5, 253, 31

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..11550

Prog

(PARI)
up_to = 11550;
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.
A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
v342417 = DirInverseCorrect(vector(up_to, n, A342002(n)));
A342417(n) = v342417[n];

Crossrefs

Cf. A342002, A342419.

Cf. A038838 (positions of even terms), A122132 (of odd terms), A353627 (parity of terms).

Cf. also A359427.

Sequence in context: A368668 A001945 A342921 * A380862 A233091 A286941

Adjacent sequences: A342414 A342415 A342416 * A342418 A342419 A342420

Keyword

sign

Author

Antti Karttunen, Mar 13 2021

Status

approved