A064141 Sum of non-unitary divisors of central binomial coefficient C(n, floor(n/2)).

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

Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..200 from Harry J. Smith)

Formula

a(n) = A048146(A001405(n)). [corrected by Amiram Eldar, Mar 07 2025]

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

Example

For n = 6, binomial(6,3) = 20 = 4*5, divisors = {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

Cf. A034448, A001405, A046098, A048146, A048243.

Sequence in context: A359001 A347802 A230926 * A230526 A156401 A246223

Adjacent sequences: A064138 A064139 A064140 * A064142 A064143 A064144

Keyword

nonn

Author

Labos Elemer, Sep 11 2001

Status

approved