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A020740
Max_{k=0..n} d(C(n,k)) - d(C(n,[ n/2 ])), where d() = number of divisors.
2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 16, 32, 0, 0, 0, 64, 48, 0, 0, 96, 0, 0, 0, 192, 256, 0, 256, 384, 0, 0, 0, 0, 0, 832, 768, 512, 0, 0, 0, 0, 384, 576, 1536, 3072, 2048, 8448, 7680, 5632, 0, 0, 0, 14336, 3584, 0, 0, 3072
OFFSET
1,18
EXAMPLE
n=20, d(C[ 20,10 ])= 48 and the d(C[ 20,k ]) values are 1,6,8,16,24,40,64,80. The maximum is 80, so the difference is 80-48 = 32.
MATHEMATICA
Table[Max[Table[DivisorSigma[0, Binomial[n, k]], {k, 0, n}]] - DivisorSigma[ 0, Binomial[n, Floor[n/2]]], {n, 70}] (* Harvey P. Dale, Jul 18 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved