%I #17 Feb 22 2023 18:04:10
%S 1,1,2,4,10,22,48,102,214,440,900,1830,3706,7486,15092,30380,61100,
%T 122780,246566,494912,992984,1991620,3993446,8005388,16044460,
%U 32150584,64414460,129037790,258462026,517641086,1036616262,2075721252,4156096036,8320912744,16658202200
%N Number of subsets of {1..n} not containing their mean.
%F a(n) = 2^n - A065795(n). - _Alois P. Heinz_, Sep 13 2019
%e The a(1) = 1 through a(5) = 22 subsets:
%e {} {} {} {} {}
%e {1,2} {1,2} {1,2} {1,2}
%e {1,3} {1,3} {1,3}
%e {2,3} {1,4} {1,4}
%e {2,3} {1,5}
%e {2,4} {2,3}
%e {3,4} {2,4}
%e {1,2,4} {2,5}
%e {1,3,4} {3,4}
%e {1,2,3,4} {3,5}
%e {4,5}
%e {1,2,4}
%e {1,2,5}
%e {1,3,4}
%e {1,4,5}
%e {2,3,5}
%e {2,4,5}
%e {1,2,3,4}
%e {1,2,3,5}
%e {1,2,4,5}
%e {1,3,4,5}
%e {2,3,4,5}
%t Table[Length[Select[Subsets[Range[n]],!MemberQ[#,Mean[#]]&]],{n,0,10}]
%o (Python)
%o from sympy import totient, divisors
%o def A327471(n): return (1<<n)-(sum((sum(totient(d)<<k//d-1 for d in divisors(k>>(~k&k-1).bit_length(),generator=True))<<1)//k for k in range(1,n+1))>>1) # _Chai Wah Wu_, Feb 22 2023
%Y Subsets containing their mean are A065795.
%Y Subsets containing n but not their mean are A327477.
%Y Partitions not containing their mean are A327472.
%Y Strict partitions not containing their mean are A240851.
%Y Cf. A000016, A007865, A051293, A067538, A082550, A114639, A135342, A324741, A327476.
%K nonn
%O 0,3
%A _Gus Wiseman_, Sep 12 2019
%E More terms from _Alois P. Heinz_, Sep 13 2019