A359779 - OEIS

%I #8 Jan 17 2023 10:01:09

%S 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 -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 -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 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 The first term with absolute value larger than 1 is a(420) = -2.

%H Antti Karttunen, <a href="/A359779/b359779.txt">Table of n, a(n) for n = 1..65537</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359778(n/d) * a(d).

%o (PARI)

%o A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 1]>f[k, 2])); };

%o A359778(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1) && (d<=m) &&

%o A359550(d), s += A359778(n/d, d))); (s));

%o memoA359779 = Map();

%o 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 Cf. A048103, A359550, A359778 (Dirichlet inverse).

%K sign

%O 1,420

%A _Antti Karttunen_, Jan 16 2023