OFFSET
1,3
COMMENTS
Equivalently, number of nonempty subsets of [n] the sum of whose elements is divisible by n. - Dimitri Papadopoulos, Jan 18 2016
FORMULA
a(n) = A063776(n) - 1.
a(n) = A008965(n) for odd n. - Dimitri Papadopoulos, Jan 18 2016
G.f.: -x/(1 - x) - Sum_{m >= 0} (phi(2*m + 1)/(2*m + 1)) * log(1 - 2*x^(2*m + 1)). - Petros Hadjicostas, Jul 13 2019
a(n) = A309402(n,n). - Alois P. Heinz, Jul 28 2019
EXAMPLE
a(5) = 7: the seven sets are (1+2+3+4+5)/5 = 3, 5/1 = 5, (1+5)/2 = 3, (1+3+5)/3 = 3, (3+5)/2 = 4, (3+4+5)/3 = 4, (1+2+4+5)/4 = 3.
MATHEMATICA
Table[Length[Select[Select[Subsets[Range[n]], Max[#]==n&], IntegerQ[ Mean[ #]]&]], {n, 22}] (* Harvey P. Dale, Jul 23 2011 *)
Table[Total[Table[Length[Select[Select[Subsets[Range[n]], Length[#] == k &], IntegerQ[Total[#]/n] &]], {k, n}]], {n, 10}] (* Dimitri Papadopoulos, Jan 18 2016 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%2)* 2^(n/d)*eulerphi(d))/n - 1; \\ Michel Marcus, Feb 10 2016
(Python)
from sympy import totient, divisors
def A082550(n): return (sum(totient(d)<<n//d-1 for d in divisors(n>>(~n&n-1).bit_length(), generator=True))<<1)//n-1 # Chai Wah Wu, Feb 22 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, May 03 2003
EXTENSIONS
a(22) from Harvey P. Dale, Jul 23 2011
a(23)-a(32) from Dimitri Papadopoulos, Jan 18 2016
STATUS
approved