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Dirichlet inverse of A238745.
2

%I #8 Jun 09 2022 11:41:35

%S 1,-2,-2,0,-2,5,-2,0,0,5,-2,-2,-2,5,5,0,-2,-2,-2,-2,5,5,-2,0,0,5,0,-2,

%T -2,-17,-2,0,5,5,5,8,-2,5,5,0,-2,-17,-2,-2,-2,5,-2,0,0,-2,5,-2,-2,0,5,

%U 0,5,5,-2,16,-2,5,-2,0,5,-17,-2,-2,5,-17,-2,-8,-2,5,-2,-2,5,-17,-2,0,0,5,-2,16,5,5,5,0,-2,16

%N Dirichlet inverse of A238745.

%H Antti Karttunen, <a href="/A354826/b354826.txt">Table of n, a(n) for n = 1..12600</a>

%H Antti Karttunen, <a href="/A354826/a354826.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} A238745(n/d) * a(d).

%o (PARI)

%o A124859(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1); factorback(f); }; \\ From A124859

%o A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));

%o A238745(n) = A181819(A124859(n));

%o memoA354826 = Map();

%o A354826(n) = if(1==n,1,my(v); if(mapisdefined(memoA354826,n,&v), v, v = -sumdiv(n,d,if(d<n,A238745(n/d)*A354826(d),0)); mapput(memoA354826,n,v); (v)));

%Y Cf. A238745.

%Y Cf. also A354349, A354359.

%K sign

%O 1,2

%A _Antti Karttunen_, Jun 09 2022