A064141 - OEIS

%I #19 Mar 22 2020 07:59:14

%S 0,0,0,0,0,12,0,0,72,328,0,768,1344,4032,3024,9072,0,36288,0,120960,

%T 322560,967680,0,1935360,6013440,15966720,43545600,104094720,

%U 163296000,362361600,149299200,447897600,1194393600,4644864000,2654208000

%N Sum of non-unitary divisors of central binomial coefficient C(n, floor(n/2)).

%H Harry J. Smith, <a href="/A064141/b064141.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) = A034448(A001405(n)).

%F If n is in A046098 then a(n)=0.

%e n=6, binomial(6,3) = 20 = 4*5, D = {1,2,4,5,10,20} of which the non-unitary divisors are 2 and 10 with Sum = a(6) = 12.

%t nus[n_] := If[n==1, 0, DivisorSigma[1, n] - Times @@ (1 + Power @@@ FactorInteger[n])]; Table[nus@ Binomial[n, Floor[n/2]], {n, 35}] (* _Giovanni Resta_, Jun 22 2018 *)

%o (PARI) usigma(n)= { my(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) }

%o a(n)={my(b=binomial(n, n\2)); sigma(b) - usigma(b);} \\ _Harry J. Smith_, Sep 08 2009

%Y Cf. A034448, A001405, A046098, A048243.

%K nonn

%O 1,6

%A _Labos Elemer_, Sep 11 2001