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A327474 Number of distinct means of subsets of {1..n}, where {} has mean 0.

%I A327474 #13 Feb 22 2023 21:24:12
%S A327474 1,2,4,6,10,16,26,38,56,78,106,138,180,226,284,348,420,500,596,698,
%T A327474 818,946,1086,1236,1408,1588,1788,2000,2230,2472,2742,3020,3328,3652,
%U A327474 3996,4356,4740,5136,5568,6018,6492,6982,7512,8054,8638,9242,9870,10520,11216
%N A327474 Number of distinct means of subsets of {1..n}, where {} has mean 0.
%F A327474 a(n) = A135342(n) + 1.
%F A327474 a(n) = 2*a(n-1) - a(n-2) + phi(n-1) for n>3. - _Chai Wah Wu_, Feb 22 2023
%e A327474 The a(3) = 6 distinct means are 0, 1, 3/2, 2, 5/2, 3.
%p A327474 a:= proc(n) option remember; `if`(n<4, [1, 2, 4, 6][n+1],
%p A327474       2*a(n-1)-a(n-2)+numtheory[phi](n-1))
%p A327474     end:
%p A327474 seq(a(n), n=0..50);  # _Alois P. Heinz_, Feb 22 2023
%t A327474 Table[Length[Union[Mean/@Subsets[Range[n]]]],{n,0,10}]
%o A327474 (Python)
%o A327474 from itertools import count, islice
%o A327474 from sympy import totient
%o A327474 def A327474_gen(): # generator of terms
%o A327474     a, b = 4, 6
%o A327474     yield from (1,2,4,6)
%o A327474     for n in count(3):
%o A327474         a, b = b, (b<<1)-a+totient(n)
%o A327474         yield b
%o A327474 A327474_list = list(islice(A327474_gen(),30)) # _Chai Wah Wu_, Feb 22 2023
%Y A327474 The version for only nonempty subsets is A135342.
%Y A327474 Cf. A000016, A051293, A065795, A082550, A327475, A327481.
%K A327474 nonn
%O A327474 0,2
%A A327474 _Gus Wiseman_, Sep 13 2019