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

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

Links

Table of n, a(n) for n=0..48.

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.

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

Sequence in context: A006305 A067247 A017985 * A347207 A028488 A280341

Adjacent sequences: A327471 A327472 A327473 * A327475 A327476 A327477

Keyword

nonn

Author

Gus Wiseman, Sep 13 2019

Status

approved