|
Search: id:A036541
|
|
|
| A036541 |
|
Deficit of central binomial coefficients in terms of number of prime factors: a[ n ] shows how many fewer prime factors the n-th central binomial coefficient has than n!. |
|
+0
1
|
|
| 0, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 4, 4, 3, 3, 5, 5, 6, 6, 6, 5, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 8
(list; graph; listen)
|
|
|
OFFSET
|
1,7
|
|
|
COMMENT
|
Primes not exceeding n/2 are missing from this kit of prime divisors. Note differences of consecutive deficits change sign like: 0,1,0,-2,0,-1,0,+2,0.
|
|
FORMULA
|
a[ n ]=PrimePi[ n ]-r[ binomial[ n, Floor[ n/2 ] ] ]=r[ n! ]-r[ binomial[ n, Floor[ n/2 ] ] ]
|
|
EXAMPLE
|
a[ 1000 ]=52 because Pi[ 1000 ]=r[ 1000! ]=168 and r[ binomial[ 1000,500 ] ]=116; so a[ 1000 ]=168-116.
|
|
CROSSREFS
|
A001405, A000720, A034973, A034974.
Sequence in context: A073454 A124765 A080356 this_sequence A036225 A069935 A062093
Adjacent sequences: A036538 A036539 A036540 this_sequence A036542 A036543 A036544
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu)
|
|
|
Search completed in 0.002 seconds
|
