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A327477 Number of subsets of {1..n} containing n whose mean is not an element.

%I A327477 #16 Feb 22 2023 01:44:49
%S A327477 0,0,1,2,6,12,26,54,112,226,460,930,1876,3780,7606,15288,30720,61680,
%T A327477 123786,248346,498072,998636,2001826,4011942,8039072,16106124,
%U A327477 32263876,64623330,129424236,259179060,518975176,1039104990,2080374784,4164816708,8337289456
%N A327477 Number of subsets of {1..n} containing n whose mean is not an element.
%F A327477 From _Alois P. Heinz_, Feb 21 2023: (Start)
%F A327477 a(n) = A327471(n) - A327471(n-1) for n>=1.
%F A327477 a(n) = 2^(n-1) - A000016(n) for n>=1. (End)
%e A327477 The a(1) = 1 through a(5) = 12 subsets:
%e A327477   {1,2}  {1,3}  {1,4}      {1,5}
%e A327477          {2,3}  {2,4}      {2,5}
%e A327477                 {3,4}      {3,5}
%e A327477                 {1,2,4}    {4,5}
%e A327477                 {1,3,4}    {1,2,5}
%e A327477                 {1,2,3,4}  {1,4,5}
%e A327477                            {2,3,5}
%e A327477                            {2,4,5}
%e A327477                            {1,2,3,5}
%e A327477                            {1,2,4,5}
%e A327477                            {1,3,4,5}
%e A327477                            {2,3,4,5}
%t A327477 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&!MemberQ[#,Mean[#]]&]],{n,0,10}]
%o A327477 (Python)
%o A327477 from sympy import totient, divisors
%o A327477 def A327477(n): return (1<<n-1)-sum(totient(d)<<n//d-1 for d in divisors(n>>(~n&n-1).bit_length(),generator=True))//n if n else 0 # _Chai Wah Wu_, Feb 21 2023
%Y A327477 Subsets whose mean is an element are A065795.
%Y A327477 Subsets whose mean is not an element are A327471.
%Y A327477 Subsets containing n whose mean is an element are A000016.
%Y A327477 Cf. A007865, A051293, A082550, A135342, A240851, A324741, A327472.
%K A327477 nonn
%O A327477 0,4
%A A327477 _Gus Wiseman_, Sep 13 2019
%E A327477 a(25)-a(34) from _Alois P. Heinz_, Feb 21 2023