A353467 - OEIS

%I #10 Apr 21 2022 17:23:22

%S 1,-1,1,2,-1,-3,1,-5,-1,3,-1,10,1,-3,1,14,-1,0,1,-10,-1,3,-1,-35,2,-3,

%T 2,10,1,3,-1,-42,1,3,-3,10,1,-3,-1,35,-1,-3,1,-10,-3,3,-1,126,-1,-9,1,

%U 10,1,-1,3,-35,-1,-3,-1,-30,1,3,3,132,-3,3,-1,-10,1,15,1,-70,-1,-3,-1,10,1,-3,1,-126,-5,3,-1,30

%N a(1) = 1, for n > 1, a(n) = -Sum_{d|n, d<n} a(A252463(n/d)) * a(d).

%H Antti Karttunen, <a href="/A353467/b353467.txt">Table of n, a(n) for n = 1..16384</a>

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

%F a(1) = 1, for n > 1, a(n) = -Sum_{d|n, d<n} A353468(n/d) * a(d).

%F For all n >= 1, a(A000040(n)) = ((-1)^n).

%o (PARI)

%o A252463(n) = if(!(n%2),n/2,my(f=factor(n)); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f));

%o memoA353467 = Map();

%o A353467(n) = if(1==n,1,my(v); if(mapisdefined(memoA353467,n,&v), v, v = -sumdiv(n,d,if(d<n,A353467(A252463(n/d))*A353467(d),0)); mapput(memoA353467,n,v); (v)));

%Y Cf. A000040, A252463, A353468 [Dirichlet inverse, also a(A252463(n))], A353469 [sum with it].

%Y Cf. also A353457.

%K sign

%O 1,4

%A _Antti Karttunen_, Apr 21 2022