A354104 Dirichlet inverse of A354102.

1, -1, -4, -1, -2, 4, -12, -1, -4, 2, -16, 4, -6, 12, 8, -1, -10, 4, -28, 2, 48, 16, -36, 4, -2, 6, -4, 12, -18, -8, -40, -1, 64, 10, 24, 4, -22, 28, 24, 2, -30, -48, -52, 16, 8, 36, -60, 4, -12, 2, 40, 6, -42, 4, 32, 12, 112, 18, -72, -8, -46, 40, 48, -1, 12, -64, -88, 10, 144, -24, -96, 4, -58, 22, 8, 28, 192, -24

Offset: 1

Author

Antti Karttunen, May 18 2022

Keywords

• sign
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..19683

Crossrefs

Cf. A023900, A267099, A267101, A354102, A354105.

Programs

PARI

A354104(n) = { my(f=factor(n)); prod(k=1,#f~,(1-A267101(primepi(f[k,1])))); }; \\ Code for A267101 can be found in A267099.

Formula

Multiplicative with a(p^e) = (1-q), where q = A267101(A000720(p)).

a(n) = A023900(A267099(n)).

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A354102(n/d) * a(d).

a(n) = A354105(n) - A354102(n).