A349337 - OEIS

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A349337

Dirichlet inverse of A230593.

1, -3, -4, 3, -6, 13, -8, -3, 4, 19, -12, -16, -14, 25, 25, 3, -18, -17, -20, -22, 33, 37, -24, 19, 6, 43, -4, -28, -30, -87, -32, -3, 49, 55, 49, 33, -38, 61, 57, 25, -42, -113, -44, -40, -29, 73, -48, -22, 8, -25, 73, -46, -54, 21, 73, 31, 81, 91, -60, 125, -62, 97, -37, 3, 85, -165, -68, -58, 97, -163, -72, -52

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OFFSET

1,2

COMMENTS

Coincides with A347084 on all squarefree numbers (A005117), but also on n=81, where a(81) = A347084(81) = 4. Question: Are there any other such numbers?

LINKS

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

FORMULA

For n > 1, a(n) = -Sum_{d|n, 1<d<n} A230593(d) * A349337(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.

A230593(n) = sumdiv(n, d, ((1==d)||isprime(d))*(n/d));

v349337 = DirInverseCorrect(vector(up_to, n, A230593(n)));

A349337(n) = v349337[n];

CROSSREFS

Cf. A005117, A069359, A230593.

Cf. also A347084, A349434, A349435.

Sequence in context: A033634 A366764 A365337 * A358045 A371858 A111970

Adjacent sequences: A349334 A349335 A349336 * A349338 A349339 A349340

KEYWORD

sign

AUTHOR

Antti Karttunen, Nov 15 2021

STATUS

approved