A346254 Dirichlet inverse of A336849.

1, -3, -5, 0, -7, 25, -11, 0, 0, 21, -13, -30, -17, 55, 35, 0, -19, -100, -23, 0, 55, 39, -29, 36, 0, 85, 0, -66, -31, -175, -37, 0, 65, 57, 77, 400, -41, 115, 85, 0, -43, -495, -47, 108, 0, 145, -53, -216, 0, 98, 171, -68, -59, 500, 169, 0, 115, 93, -61, 210, -67, 111, 0, 0, 119, -325, -71, 0, 261, -385, -73, -120, -79, 205, 0, -138

Offset

1,2

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A346255(n) - A336849(n).

Prog

(PARI)
up_to = 16384;
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.
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A336849(n) = { my(u=A003961(n)); (u/gcd(u, sigma(u))); };
v346254 = DirInverseCorrect(vector(up_to, n, A336849(n)));
A346254(n) = v346254[n];

Crossrefs

Cf. A000203, A003961, A003973, A336849, A346255, A346256 (positions of zeros).

Cf. also A346235, A346246, A346248.

Sequence in context: A229984 A346234 A346479 * A021289 A200480 A099895

Adjacent sequences: A346251 A346252 A346253 * A346255 A346256 A346257

Keyword

sign

Author

Antti Karttunen, Jul 19 2021

Status

approved