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A081387 Number of non-unitary prime divisors of central binomial coefficient, C(2n,n) = A000984(n), i.e., number of prime factors in C(2n,n) whose exponent is greater than one. 8
0, 0, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 2, 2, 2, 2, 1, 1, 3, 3, 3, 3, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 3, 3, 3, 2, 4, 2, 2, 3, 3, 3, 3, 4, 4, 5, 4, 4, 2, 3, 3, 2, 2, 2, 4, 3, 3, 4, 3, 4, 5, 4, 2, 2, 2, 3, 5, 5, 5, 5, 3, 2, 3, 2, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A056170(A000984(n)) = A001221(A000984(n)) - A081386(n)= A067434(n) - A081386(n).

EXAMPLE

For n=14: binomial(28,14) = 40116600 = 2*2*2*3*3*3*5*5*17*19*23;

unitary prime divisors: {17,19,23};

non-unitary prime divisors: {2,3,5}, so a(14)=3.

MATHEMATICA

Table[Count[Transpose[FactorInteger[Binomial[2n, n]]][[2]], _?(#>1&)], {n, 110}] (* Harvey P. Dale, Oct 08 2012 *)

CROSSREFS

Cf. A000984, A034444, A048105, A056169, A056170, A067434, A081387-A081389.

Sequence in context: A116531 A101871 A101875 * A261795 A306345 A204125

Adjacent sequences:  A081384 A081385 A081386 * A081388 A081389 A081390

KEYWORD

nonn

AUTHOR

Labos Elemer, Mar 27 2003

STATUS

approved

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Last modified August 9 13:57 EDT 2020. Contains 336323 sequences. (Running on oeis4.)