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A327474
Number of distinct means of subsets of {1..n}, where {} has mean 0.
6
1, 2, 4, 6, 10, 16, 26, 38, 56, 78, 106, 138, 180, 226, 284, 348, 420, 500, 596, 698, 818, 946, 1086, 1236, 1408, 1588, 1788, 2000, 2230, 2472, 2742, 3020, 3328, 3652, 3996, 4356, 4740, 5136, 5568, 6018, 6492, 6982, 7512, 8054, 8638, 9242, 9870, 10520, 11216
OFFSET
0,2
FORMULA
a(n) = A135342(n) + 1.
a(n) = 2*a(n-1) - a(n-2) + phi(n-1) for n>3. - Chai Wah Wu, Feb 22 2023
EXAMPLE
The a(3) = 6 distinct means are 0, 1, 3/2, 2, 5/2, 3.
MAPLE
a:= proc(n) option remember; `if`(n<4, [1, 2, 4, 6][n+1],
2*a(n-1)-a(n-2)+numtheory[phi](n-1))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Feb 22 2023
MATHEMATICA
Table[Length[Union[Mean/@Subsets[Range[n]]]], {n, 0, 10}]
PROG
(Python)
from itertools import count, islice
from sympy import totient
def A327474_gen(): # generator of terms
a, b = 4, 6
yield from (1, 2, 4, 6)
for n in count(3):
a, b = b, (b<<1)-a+totient(n)
yield b
A327474_list = list(islice(A327474_gen(), 30)) # Chai Wah Wu, Feb 22 2023
CROSSREFS
The version for only nonempty subsets is A135342.
Sequence in context: A006305 A067247 A017985 * A347207 A028488 A280341
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 13 2019
STATUS
approved