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A368694 Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).

%I A368694 #12 Jan 04 2024 14:45:38
%S A368694 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 A368694 -30,-8,16,0,32,8,-4,0,-1144,-272,20,0,32,8,-512,0,45,12,-126,0,-252,
%U A368694 -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 A368694 Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).
%C A368694 Scatter plot: "Sailboard congestion".
%H A368694 Antti Karttunen, <a href="/A368694/b368694.txt">Table of n, a(n) for n = 0..16384</a>
%F A368694 a(n) = A366889(A163511(n)).
%o A368694 (PARI)
%o A368694 A082903(n) = (2^valuation(sigma(n), 2));
%o A368694 memoA366889 = Map();
%o A368694 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 A368694 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 A368694(n) = A366889(A163511(n));
%Y A368694 Cf. A163511, A082903, A366889, A368695 (rgs-transform).
%K A368694 sign,look
%O A368694 0,4
%A A368694 _Antti Karttunen_, Jan 03 2024