A048299 -id:A048299 - cp's OEIS frontend

A048484 a(n) = abs(floor(n/2) - A048299(n)).

0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 1, 0, 0, 2, 3, 0, 0, 3, 3, 2, 2, 3, 3, 2, 7, 7, 1, 4, 4, 6, 5, 4, 4, 1, 2, 2, 2, 1, 1, 0, 0, 3, 3, 2, 6, 10, 7, 5, 4, 10, 5, 9, 8, 6, 3, 8, 7, 8, 8, 2, 1, 10, 10, 0, 0, 5, 4, 2, 2, 3, 7, 8, 7, 5, 5, 6, 3, 7, 7, 8, 4, 5, 6, 6, 11, 11, 10, 10, 4, 9, 8, 8, 7, 7, 6, 6, 5, 7, 13, 15

Offset: 1

Labos Elemer

nonn

			If n = 100 then the number of distinct primes at central C(100, 50) coefficient is 15, while the maximal is 18 which appears first at k = 35. Thus a(100) = 50 - 35 = 15.

Cf. A001221, A001405, A034974, A048275.

Table[Abs@ Floor[n/2] - Min@ MaximalBy[Range[0, n], PrimeNu@ Binomial[n, #] &], {n, 100}] (* Michael De Vlieger, Aug 01 2017 *)

A020731 Numbers n for which number of distinct prime divisors of C(n,k) has maximum at k = [n/2].

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 43, 47, 48, 49, 50, 55, 56, 57, 58, 63, 64, 65, 66, 67, 68, 71, 72, 73, 75, 76, 80, 83, 84, 85, 89, 90, 96, 97, 98, 99, 100, 107, 108, 109, 119

Offset: 1

Labos Elemer

nonn

			For n=21 the number of prime divisors of {C(21,k)} is {0,2,4,4,4,4,5,5,6,6,6,6,6,6,5,5,4,4,4,4,2,0}, the maximal value of 6 occurring at the central position.

Ivan Neretin, Table of n, a(n) for n = 1..1000

Cf. A001221, A048486, A048299, A048484, A019491.

Select[Range[120], Function[n, ar = PrimeNu[Binomial[n, Range[0, n/2]]]; Max[ar] == ar[[-1]]]] (* Ivan Neretin, Aug 14 2015 *)

cp's OEIS Frontend

A048484 a(n) = abs(floor(n/2) - A048299(n)).

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