OFFSET
1,6
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
For n = 14, binomial(14,7) = 3432 has 32 divisors, 16 unitary, 16 squarefree. The size of overlap is 8. The complementary parts are: non-unitary/squarefree set ={2,6,22,26,66,78,286,828}, while the unitary/not squarefree set of equal size is {8,24,88,104,264,312,1144,3432}. So a(14) = 8.
MATHEMATICA
f[p_, e_] := If[e == 1, 2, 1]; a[1] = 0; a[n_] := 2^Length[fct = FactorInteger[Binomial[n, Floor[n/2]]]] - Times @@ f @@@ fct; Array[a, 100] (* Amiram Eldar, Oct 04 2024 *)
PROG
(PARI) a(n) = {my(f = factor(binomial(n, n\2)), e = f[, 2]); 2^omega(f) - prod(i = 1, #e, if(e[i] == 1, 2, 1)); } \\ Amiram Eldar, Oct 04 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 10 2000
STATUS
approved