A327474 - OEIS

%I #13 Feb 22 2023 21:24:12

%S 1,2,4,6,10,16,26,38,56,78,106,138,180,226,284,348,420,500,596,698,

%T 818,946,1086,1236,1408,1588,1788,2000,2230,2472,2742,3020,3328,3652,

%U 3996,4356,4740,5136,5568,6018,6492,6982,7512,8054,8638,9242,9870,10520,11216

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

%F a(n) = A135342(n) + 1.

%F a(n) = 2*a(n-1) - a(n-2) + phi(n-1) for n>3. - _Chai Wah Wu_, Feb 22 2023

%e The a(3) = 6 distinct means are 0, 1, 3/2, 2, 5/2, 3.

%p a:= proc(n) option remember; `if`(n<4, [1, 2, 4, 6][n+1],

%p       2*a(n-1)-a(n-2)+numtheory[phi](n-1))

%p     end:

%p seq(a(n), n=0..50);  # _Alois P. Heinz_, Feb 22 2023

%t Table[Length[Union[Mean/@Subsets[Range[n]]]],{n,0,10}]

%o (Python)

%o from itertools import count, islice

%o from sympy import totient

%o def A327474_gen(): # generator of terms

%o     a, b = 4, 6

%o     yield from (1,2,4,6)

%o     for n in count(3):

%o         a, b = b, (b<<1)-a+totient(n)

%o         yield b

%o A327474_list = list(islice(A327474_gen(),30)) # _Chai Wah Wu_, Feb 22 2023

%Y The version for only nonempty subsets is A135342.

%Y Cf. A000016, A051293, A065795, A082550, A327475, A327481.

%K nonn

%O 0,2

%A _Gus Wiseman_, Sep 13 2019