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A329892 a(0) = 0, a(1) = 1, for n > 1, a(n) = 2^(n+1) - 3*(sigma((2^n)-1) - sigma((2^(n-1))-1)).

%I A329892 #11 Dec 11 2019 20:11:14
%S A329892 0,1,-1,4,-16,40,-88,184,-400,544,-784,2224,-11536,18016,-10240,16384,
%T A329892 -86560,203296,-503296,896512,-2329600,2795776,-1942528,8805088,
%U A329892 -54906208,77129728,-30207616,70521376,-383472160,840798784,-2278740544,3898507264,-6881424448,8016635968,-3284792320,28687532032,-252678823936,359583387328,-135598386880
%N A329892 a(0) = 0, a(1) = 1, for n > 1, a(n) = 2^(n+1) - 3*(sigma((2^n)-1) - sigma((2^(n-1))-1)).
%H A329892 Antti Karttunen, <a href="/A329892/b329892.txt">Table of n, a(n) for n = 0..255</a>
%H A329892 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A329892 a(n) = A329644(3^n).
%F A329892 a(0) = 0; for n >= 1, a(n) = 2^(n+1) - 3*A329890(n).
%o A329892 (PARI)
%o A329892 A329890(n) = if(1==n,1,sigma((2^n)-1)-sigma((2^(n-1))-1));
%o A329892 A329892(n) = if(!n,n,2^(n+1) - 3*A329890(n));
%o A329892 (PARI)
%o A329892 A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A329892 A323243(n) = if(1==n, 0, sigma(A156552(n)));
%o A329892 A329644(n) = sumdiv(n, d, moebius(n/d)*((2*A156552(d))-A323243(d)));
%o A329892 A329892(n) = A329644(3^n);
%Y A329892 Row 2 of A329637.
%Y A329892 Cf. A000203, A000225, A075708, A156552, A323243, A329644, A329890, A329891.
%K A329892 sign
%O A329892 0,4
%A A329892 _Antti Karttunen_, Nov 23 2019