%I #6 Oct 27 2023 13:11:56

%S 1,-1,0,-3,0,1,3,-4,0,-1,-1,-1,0,10,4,-5,0,-2,1,-8,0,5,1,-5,0,-2,-10,

%T 14,0,12,5,-7,0,-4,2,-24,0,32,8,-27,0,1,-5,26,0,18,5,-19,0,6,2,11,0,

%U -20,-14,20,0,-2,-12,18,0,16,7,-8,0,-8,4,-72,0,112,24,-108,0,-8,-32,162,0,108,27,-125,0,3,-1,35,0

%N a(n) = A349915(A163511(n)), where A349915 is the Dirichlet inverse of the arithmetic mean between the number and sum of the odd divisors of n.

%H Antti Karttunen, <a href="/A366875/b366875.txt">Table of n, a(n) for n = 0..16384</a>

%o (PARI)

%o A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

%o A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));

%o memoA349915 = Map();

%o A349915(n) = if(1==n,1,my(v); if(mapisdefined(memoA349915,n,&v), v, v = -sumdiv(n,d,if(d<n,A113415(n/d)*A349915(d),0)); mapput(memoA349915,n,v); (v)));

%o A366875(n) = A349915(A163511(n));

%Y Cf. A113415, A163511, A349915, A366878 (rgs-transform).

%Y Cf. also A366873.

%K sign

%O 0,4

%A _Antti Karttunen_, Oct 27 2023