A354104 - OEIS

%I #11 May 19 2022 09:21:14

%S 1,-1,-4,-1,-2,4,-12,-1,-4,2,-16,4,-6,12,8,-1,-10,4,-28,2,48,16,-36,4,

%T -2,6,-4,12,-18,-8,-40,-1,64,10,24,4,-22,28,24,2,-30,-48,-52,16,8,36,

%U -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

%N Dirichlet inverse of A354102.

%H Antti Karttunen, <a href="/A354104/b354104.txt">Table of n, a(n) for n = 1..19683</a>

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

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

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

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

%o (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.

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

%K sign,mult

%O 1,3

%A _Antti Karttunen_, May 18 2022