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A324865 a(n) = A323243(n) - A156552(n).

%I A324865 #5 Mar 18 2019 21:49:25
%S A324865 0,0,1,1,3,1,7,1,6,4,15,1,31,1,8,9,63,1,127,1,21,15,255,1,16,19,10,13,
%T A324865 511,11,1023,1,20,47,22,13,2047,1,78,17,4095,1,8191,1,14,287,16383,1,
%U A324865 36,6,122,1,32767,1,55,1,270,277,65535,1,131071,687,22,41,58,27,262143,45,260,1,524287,17,1048575,259,16
%N A324865 a(n) = A323243(n) - A156552(n).
%H A324865 Antti Karttunen, <a href="/A324865/b324865.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A324865 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324865 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324865 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324865 a(1) = 0; for n > 1, a(n) = A001065(A156552(n)).
%F A324865 a(n) = A323243(n) - A156552(n).
%o A324865 (PARI)
%o A324865 A001065(n) = (sigma(n)-n);
%o A324865 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 A324865 A324865(n) = if(1==n,0,A001065(A156552(n)));
%o A324865 (PARI) A324865(n) = (A323243(n) - A156552(n)); \\ Needs also code from A323243.
%Y A324865 Cf. A001065, A156552, A323243, A324866, A324867, A324868.
%K A324865 nonn
%O A324865 1,5
%A A324865 _Antti Karttunen_, Mar 18 2019