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A036541
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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!.
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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; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| 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.
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FORMULA
| a[ n ]=PrimePi[ n ]-r[ binomial[ n, Floor[ n/2 ] ] ]=r[ n! ]-r[ binomial[ n, Floor[ n/2 ] ] ]
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EXAMPLE
| a[ 1000 ]=52 because Pi[ 1000 ]=r[ 1000! ]=168 and r[ binomial[ 1000,500 ] ]=116; so a[ 1000 ]=168-116.
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CROSSREFS
| A001405, A000720, A034973, A034974.
Sequence in context: A080356 A191408 A184167 * A176505 A036225 A069935
Adjacent sequences: A036538 A036539 A036540 * A036542 A036543 A036544
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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