A324640 Dirichlet inverse of the Doudna sequence, A005940.

1, -2, -3, 0, -5, 6, -9, 0, 2, 10, -15, 0, -25, 18, 3, 0, -11, -4, -21, 0, 19, 30, -45, 0, -24, 50, -60, 0, -125, -6, -81, 0, 77, 22, 57, 0, -55, 42, 87, 0, -77, -38, -105, 0, -78, 90, -135, 0, -40, 48, -81, 0, -245, 120, -75, 0, -217, 250, -375, 0, -625, 162, -150, 0, 233, -154, -39, 0, 205, -114, -99, 0, -91, 110, 174, 0, -5, -174, -189, 0

Offset: 1

Author

Antti Karttunen, Mar 11 2019

Keywords

• sign

Links

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

Crossrefs

Cf. A005940, A324106, A324641.

Programs

PARI

up_to = 16384;
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(dA005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
v324640 = DirInverse(vector(up_to,n,A005940(n)));
A324640(n) = v324640[n];

Formula

a(1) = 1; for n > 1, a(n) = -Sum_{d|n, dA005940(n/d).

a(p) = -A005940(p) for all primes p.