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A329641 a(n) = gcd(A329638(n), A329639(n)).

%I A329641 #8 Nov 22 2019 18:53:53
%S A329641 0,1,1,2,1,4,1,6,1,5,1,10,1,16,2,6,1,1,1,18,1,18,1,22,1,46,1,22,1,10,
%T A329641 1,30,14,82,2,1,1,256,2,22,1,1,1,66,1,226,1,46,1,1,8,130,1,1,1,70,2,
%U A329641 748,1,42,1,1362,2,2,10,42,1,214,254,4,1,1,1,3838,5,406,2,2,1,78,1,5458,1,26,2,12250,2,10,1,2,1,934
%N A329641 a(n) = gcd(A329638(n), A329639(n)).
%H A329641 Antti Karttunen, <a href="/A329641/b329641.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A329641 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A329641 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329641 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A329641 a(n) = gcd(A329638(n), A329639(n)).
%F A329641 a(A324201(n)) = A329610(n).
%o A329641 (PARI)
%o A329641 A323243(n) = if(1==n,0,sigma(A156552(n)));
%o A329641 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 A329641 A329644(n) = sumdiv(n,d,moebius(n/d)*((2*A156552(d))-A323243(d)));
%o A329641 A329641(n) = { my(t=0,u=0); fordiv(n, d, if((d=A329644(d))>0, t +=d, u -= d)); gcd(u,t); };
%Y A329641 Cf. A156552, A323243, A324201, A329610, A329638, A329639, A329640, A329644.
%K A329641 nonn
%O A329641 1,4
%A A329641 _Antti Karttunen_, Nov 22 2019