A354365 Numerators of Dirichlet inverse of primorial deflation fraction A319626(n) / A319627(n).

1, -2, -3, 0, -5, 3, -7, 0, 0, 10, -11, 0, -13, 14, 5, 0, -17, 0, -19, 0, 21, 22, -23, 0, 0, 26, 0, 0, -29, -5, -31, 0, 33, 34, 7, 0, -37, 38, 39, 0, -41, -21, -43, 0, 0, 46, -47, 0, 0, 0, 51, 0, -53, 0, 55, 0, 57, 58, -59, 0, -61, 62, 0, 0, 65, -33, -67, 0, 69, -14, -71, 0, -73, 74, 0, 0, 11, -39, -79, 0, 0, 82

Offset

1,2

Comments

Because the ratio n / A064989(n) = A319626(n) / A319627(n) is multiplicative, so is also its Dirichlet inverse (which also is a sequence of rational numbers). This sequence gives the numerators when presented in its lowest terms, while A354366 gives the denominators. See the examples.

Links

Table of n, a(n) for n=1..82.

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A055615(n) / gcd(A055615(n), A064989(n)).

Example

The ratio a(n)/A354366(n) for n = 1..22: 1, -2, -3/2, 0, -5/3, 3, -7/5, 0, 0, 10/3, -11/7, 0, -13/11, 14/5, 5/2, 0, -17/13, 0, -19/17, 0, 21/10, 22/7.

Prog

(PARI)
A064989(n) = { my(f = factor(n)); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A354365(n) = numerator((moebius(n)*n)/A064989(n));

Crossrefs

Cf. A013929 (positions of 0's), A055615, A319626, A319627, A354350.

Cf. A354366 (denominators).

Cf. also A349629, A354351, A354827.

Sequence in context: A197658 A199514 A080367 * A066913 A090303 A277516

Adjacent sequences: A354362 A354363 A354364 * A354366 A354367 A354368

Keyword

sign,frac

Author

Antti Karttunen, Jun 07 2022

Status

approved