login
a(n) = A048106(A001405(n)).
1

%I #19 Oct 05 2024 09:07:50

%S 1,2,2,4,4,2,4,8,4,-2,16,8,8,0,8,16,32,16,32,16,32,0,64,32,-16,-64,

%T -160,-256,-128,-224,64,128,0,-256,256,-128,-128,-512,512,-256,512,0,

%U 512,0,-2048,-2816,-256,-1408,-1408,-2560,-2560,-4096,-1024,-1792,2048

%N a(n) = A048106(A001405(n)).

%C The terms indicate whether more, equal or fewer unitary than non-unitary divisors of the central binomial coefficient exists.

%H Amiram Eldar, <a href="/A048244/b048244.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A034444(A001405(n)) - A048105(A001405(n)).

%e For n = 54, binomial(54,27) has 3840 divisors of which 1024 are unitary and 2816 are not. The difference is -1792, so a(54) = -1792.

%t a[n_] := Module[{b = Binomial[n, Floor[n/2]]}, 2^(PrimeNu[b] + 1) - DivisorSigma[0, b]]; Array[a, 60] (* _Amiram Eldar_, Oct 05 2024 *)

%o (PARI) a048106(n) = (2^(1+omega(n)) - numdiv(n));

%o a(n) = a048106(binomial(n, n\2)); \\ _Michel Marcus_, May 14 2018

%Y Cf. A001405, A048106.

%K sign

%O 1,2

%A _Labos Elemer_