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%I #8 Jun 09 2022 11:41:32
%S 1,-2,-2,1,-2,4,-2,-2,1,4,-2,-2,-2,4,4,8,-2,-2,-2,-2,4,4,-2,4,1,4,-2,
%T -2,-2,-8,-2,-16,4,4,4,1,-2,4,4,4,-2,-8,-2,-2,-2,4,-2,-16,1,-2,4,-2,
%U -2,4,4,4,4,4,-2,4,-2,4,-2,20,4,-8,-2,-2,4,-8,-2,-2,-2,4,-2,-2,4,-8,-2,-16,8,4,-2,4,4,4,4,4
%N Dirichlet inverse of A293442, where A293442 is multiplicative with a(p^e) = A019565(e).
%C Multiplicative because A293442 is.
%H Antti Karttunen, <a href="/A354825/b354825.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A354825/a354825.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A293442(n/d) * a(d).
%o (PARI)
%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A293442(n) = factorback(apply(e -> A019565(e),factor(n)[,2]));
%o memoA354825 = Map();
%o A354825(n) = if(1==n,1,my(v); if(mapisdefined(memoA354825,n,&v), v, v = -sumdiv(n,d,if(d<n,A293442(n/d)*A354825(d),0)); mapput(memoA354825,n,v); (v)));
%Y Cf. A019565, A293442.
%K sign,mult
%O 1,2
%A _Antti Karttunen_, Jun 09 2022
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