A048622 Difference of maximal and central values of A001222 when applied to {C(n,k)} set.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 3, 2, 1, 1, 3, 2, 1, 0, 2, 1, 2, 1, 1, 0, 0, 0, 2, 2, 1, 0, 1, 1, 3, 2, 3, 2, 0, 0, 2, 0, 0, 0, 4, 3, 4, 3, 2, 2, 3, 3, 5, 4, 3, 2, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 0, 0, 1, 1, 3, 2, 1, 0, 0, 0, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2

Offset

1,18

Links

Michel Marcus, Table of n, a(n) for n = 1..5000

Formula

a(n) = Max_k {A001222(C(n, k))} - A001222(A001405(n)).

a(n) = A048620(n) - A048621(n). - Sean A. Irvine, Jun 24 2021

Example

n=24: the sums of prime factor exponents when k runs from 0 to 24 are {0,4,4,5,5,7,6,8,6,8,8,9,7,9,8,8,6,8,6,7,5,5,4,4,0}. The central value is 7, the maximal is 9 so a(24)=9-7.

Prog

(PARI) a(n) = vecmax(apply(bigomega, vector(n+1, k, binomial(n, k-1)))) - bigomega(binomial(n, n\2)); \\ Michel Marcus, Jun 25 2021

Crossrefs

Cf. A001222, A046660, A020740, A048620, A048621.

Sequence in context: A226518 A337518 A073781 * A105661 A082451 A121362

Adjacent sequences: A048619 A048620 A048621 * A048623 A048624 A048625

Keyword

nonn

Author

Labos Elemer

Status

approved