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A064141
Sum of non-unitary divisors of central binomial coefficient C(n, floor(n/2)).
1
0, 0, 0, 0, 0, 12, 0, 0, 72, 328, 0, 768, 1344, 4032, 3024, 9072, 0, 36288, 0, 120960, 322560, 967680, 0, 1935360, 6013440, 15966720, 43545600, 104094720, 163296000, 362361600, 149299200, 447897600, 1194393600, 4644864000, 2654208000
OFFSET
1,6
LINKS
FORMULA
a(n) = A034448(A001405(n)).
If n is in A046098 then a(n)=0.
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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) }
a(n)={my(b=binomial(n, n\2)); sigma(b) - usigma(b); } \\ Harry J. Smith, Sep 08 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 11 2001
STATUS
approved