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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 Michael De Vlieger, Table of n, a(n) for n = 1..10000 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 Cf. A001221, A001405, A034444, A034973, A039593, A056057, A056173. Sequence in context: A059282 A114591 A161849 * A325987 A105241 A134541 Adjacent sequences:  A056172 A056173 A056174 * A056176 A056177 A056178 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 July 31 15:25 EDT 2021. Contains 346374 sequences. (Running on oeis4.)