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A359779 Dirichlet inverse of A359778, where A359778 is the number of factorizations of n into factors not divisible by p^p for any prime p (terms of A048103).

%I A359779 #8 Jan 17 2023 10:01:09
%S A359779 1,-1,-1,0,-1,0,-1,0,-1,0,-1,1,-1,0,0,0,-1,1,-1,1,0,0,-1,0,-1,0,1,1,
%T A359779 -1,1,-1,0,0,0,0,0,-1,0,0,0,-1,1,-1,1,1,0,-1,0,-1,1,0,1,-1,1,0,0,0,0,
%U A359779 -1,0,-1,0,1,0,0,1,-1,1,0,1,-1,0,-1,0,1,1,0,1,-1,0,0,0,-1,0,0,0,0,0,-1,1,0,1,0,0,0,0,-1,1,1,0,-1,1,-1,0,1
%N A359779 Dirichlet inverse of A359778, where A359778 is the number of factorizations of n into factors not divisible by p^p for any prime p (terms of A048103).
%C A359779 The first term with absolute value larger than 1 is a(420) = -2.
%H A359779 Antti Karttunen, <a href="/A359779/b359779.txt">Table of n, a(n) for n = 1..65537</a>
%F A359779 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359778(n/d) * a(d).
%o A359779 (PARI)
%o A359779 A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 1]>f[k, 2])); };
%o A359779 A359778(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1) && (d<=m) &&
%o A359779 A359550(d), s += A359778(n/d, d))); (s));
%o A359779 memoA359779 = Map();
%o A359779 A359779(n) = if(1==n,1,my(v); if(mapisdefined(memoA359779,n,&v), v, v = -sumdiv(n,d,if(d<n,A359778(n/d)*A359779(d),0)); mapput(memoA359779,n,v); (v)));
%Y A359779 Cf. A048103, A359550, A359778 (Dirichlet inverse).
%K A359779 sign
%O A359779 1,420
%A A359779 _Antti Karttunen_, Jan 16 2023