A379110 - OEIS

%I #6 Dec 17 2024 08:24:15

%S 1,-2,-1,0,-1,2,-1,7,-8,2,-1,0,-1,2,1,-28,-1,16,-1,0,1,2,-1,-7,-24,2,

%T 16,0,-1,-2,-1,59,1,2,1,0,-1,2,1,-7,-1,-2,-1,0,8,2,-1,28,0,48,1,0,-1,

%U -32,1,-7,1,2,-1,0,-1,2,8,-75,1,-2,-1,0,1,-2,-1,-56,-1,2,24,0,1,-2,-1,28,56,2,-1,0,1,2,1,-7

%N Dirichlet inverse of A324892, where A324892 is multiplicative with a(p^e) = p^e if sigma(p^e) is prime, and 1 otherwise.

%H Antti Karttunen, <a href="/A379110/b379110.txt">Table of n, a(n) for n = 1..32769</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A324892(n/d) * a(d).

%o (PARI)

%o A324892(n) = { my(f=factor(n)); prod(i=1, #f~, (f[i,1]^isprime(sigma(f[i,1]^f[i,2])))^f[i,2]); };

%o memoA379110 = Map();

%o A379110(n) = if(1==n,1,my(v); if(mapisdefined(memoA379110,n,&v), v, v = -sumdiv(n,d,if(d<n,A324892(n/d)*A379110(d),0)); mapput(memoA379110,n,v); (v)));

%Y Cf. A000203, A324892.

%K sign,mult

%O 1,2

%A _Antti Karttunen_, Dec 17 2024