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%I #12 Nov 22 2019 18:53:33
%S 0,1,1,2,1,4,1,6,1,5,1,10,1,16,2,6,1,13,1,18,2,18,1,22,1,46,5,22,1,10,
%T 1,30,14,82,2,19,1,256,2,22,1,41,1,66,9,226,1,46,1,24,8,130,1,29,2,70,
%U 2,748,1,42,1,1362,22,30,10,42,1,214,254,44,1,43,1,3838,15,406,2,120,1,78,5,5458,1,52,2,12250,2,70,1,26,2,934
%N Sum of A329644(d) for all such divisors d of n for which that value is positive. Here A329644 is the Möbius transform of A323244, the deficiency of A156552(n).
%H Antti Karttunen, <a href="/A329638/b329638.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = Sum_{d|n} [A329644(d) > 0] * A329644(d), where [ ] is Iverson bracket.
%F a(n) = A323244(n) + A329639(n).
%o (PARI)
%o 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 A323243(n) = if(1==n,0,sigma(A156552(n)));
%o A324543(n) = sumdiv(n,d,moebius(n/d)*A323243(d));
%o A297113(n) = if(1==n, 0, (primepi(vecmax(factor(n)[, 1])) + (bigomega(n)-omega(n))));
%o A329644(n) = if(1==n,0, 2^A297113(n) - A324543(n));
%o A329638(n) = sumdiv(n,d,if((d=A329644(d))>0,d,0));
%Y Cf. A156552, A323243, A323244, A329639, A329641, A329644.
%Y Cf. also A318878.
%K nonn
%O 1,4
%A _Antti Karttunen_, Nov 21 2019