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A056175 Number of nonunitary prime divisors of the central binomial coefficient C(n, floor(n/2)) (A001405). 6
0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 3, 3, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 0, 1, 1, 1, 2, 2, 3, 3, 1, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,10
COMMENTS
Number of prime divisors of the largest square dividing A001405(n). (A prime divisor is nonunitary iff its exponent exceeds 1.)
LINKS
FORMULA
a(n) = A001221(A000188(A001405(n))).
a(n) = A001221(A056057(n)).
EXAMPLE
For n=10, binomial(10, 5) = 252 = 2*2*3*3*7 has 3 prime divisors of which only one, p=7, is unitary, while 2 and 3 are not. So a(10)=2.
For n=256, binomial(256, 128) also has only 2 prime divisors (3 and 13) whose exponents exceed 1 (4 and 2, respectively), thus a(256)=2.
MATHEMATICA
Table[Count[FactorInteger[Binomial[n, Floor[n/2]]][[All, -1]], e_ /; e > 1], {n, 105}] (* Michael De Vlieger, Mar 05 2017 *)
PROG
(PARI) a(n)=omega(core(binomial(n, n\2), 1)[2]) \\ Charles R Greathouse IV, Mar 09 2017
CROSSREFS
Sequence in context: A059282 A114591 A161849 * A325987 A359324 A353421
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 27 2000
EXTENSIONS
Edited by Jon E. Schoenfield, Mar 05 2017
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)