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Dirichlet inverse of A038548, where A038548 is the number of divisors of n that are at most sqrt(n).
1

%I #10 Jan 27 2024 10:32:25

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

%T -1,2,-1,0,0,0,0,1,-1,0,0,0,-1,2,-1,2,2,0,-1,-1,-1,2,0,2,-1,0,0,0,0,0,

%U -1,0,-1,0,2,0,0,2,-1,2,0,2,-1,-3,-1,0,2,2,0,2,-1,-1,0,0,-1,0,0,0,0,0,-1,0,0,2,0,0,0,0,-1,2,2

%N Dirichlet inverse of A038548, where A038548 is the number of divisors of n that are at most sqrt(n).

%H Antti Karttunen, <a href="/A369453/b369453.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} A038548(n/d) * a(d).

%F Dirichlet g.f.: 2/(zeta(s)^2 + zeta(2*s)).

%o (PARI)

%o A038548(n) = if( n<1, 0, sumdiv(n, d, d*d <= n))

%o memoA369453 = Map();

%o A369453(n) = if(1==n,1,my(v); if(mapisdefined(memoA369453,n,&v), v, v = -sumdiv(n,d,if(d<n,A038548(n/d)*A369453(d),0)); mapput(memoA369453,n,v); (v)));

%Y Cf. A038548.

%Y Cf. also A359763, A369454.

%K sign

%O 1,12

%A _Antti Karttunen_, Jan 27 2024