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Dirichlet inverse of A364557, which is Möbius transform of A005941.
2

%I #11 Aug 30 2023 13:03:41

%S 1,-1,-2,-1,-4,2,-8,-1,0,4,-16,2,-32,8,12,-1,-64,0,-128,4,24,16,-256,

%T 2,8,32,0,8,-512,-12,-1024,-1,48,64,56,0,-2048,128,96,4,-4096,-24,

%U -8192,16,-8,256,-16384,2,48,-8,192,32,-32768,0,112,8,384,512,-65536,-12,-131072,1024,-16,-1,224,-48,-262144,64,768

%N Dirichlet inverse of A364557, which is Möbius transform of A005941.

%H Antti Karttunen, <a href="/A364952/b364952.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A364557(n/d) * a(d).

%F a(p) = -A000079(A000720(p)-1) for all primes p.

%o (PARI)

%o A364557(n) = if(1==n, 1, 2^(primepi(vecmax(factor(n)[, 1]))+(bigomega(n)-omega(n))-1));

%o memoA364952 = Map();

%o A364952(n) = if(1==n,1,my(v); if(mapisdefined(memoA364952,n,&v), v, v = -sumdiv(n,d,if(d<n,A364557(n/d)*A364952(d),0)); mapput(memoA364952,n,v); (v)));

%Y Cf. A000079, A000720, A005941, A364557, A364953.

%Y Cf. also A364574.

%K sign

%O 1,3

%A _Antti Karttunen_, Aug 29 2023