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Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).
2

%I #12 Jan 04 2024 14:45:38

%S 1,-1,0,-4,0,15,4,-2,0,-64,-15,3,0,8,2,-8,0,272,64,-8,0,-12,-3,63,0,

%T -30,-8,16,0,32,8,-4,0,-1144,-272,20,0,32,8,-512,0,45,12,-126,0,-252,

%U -63,15,0,128,30,-24,0,-64,-16,32,0,-120,-32,8,0,16,4,-2,0,4816,1144,-44,0,-80,-20,4160,0,-120,-32,1024,0

%N Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).

%C Scatter plot: "Sailboard congestion".

%H Antti Karttunen, <a href="/A368694/b368694.txt">Table of n, a(n) for n = 0..16384</a>

%F a(n) = A366889(A163511(n)).

%o (PARI)

%o A082903(n) = (2^valuation(sigma(n), 2));

%o memoA366889 = Map();

%o A366889(n) = if(1==n,1,my(v); if(mapisdefined(memoA366889,n,&v), v, v = -sumdiv(n,d,if(d<n,A082903(n/d)*A366889(d),0)); mapput(memoA366889,n,v); (v)));

%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 A368694(n) = A366889(A163511(n));

%Y Cf. A163511, A082903, A366889, A368695 (rgs-transform).

%K sign,look

%O 0,4

%A _Antti Karttunen_, Jan 03 2024