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A081389 Number of non-unitary prime divisors of Catalan numbers, i.e., number of those prime factors whose exponent is greater than one. 6
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 2, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2, 3, 2, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 2, 1, 3, 3, 3, 2, 4, 4, 4, 4, 2, 2, 3, 1, 1, 2, 2, 3, 2, 3, 3, 2, 4, 4, 2, 2, 2, 2, 3, 4, 5, 4, 3, 2, 2, 2, 2, 2, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A056170(A000108(n)).

EXAMPLE

For n=25: Catalan(25) = binomial(50,25)/26 = 4861946401452 =(2*2*3*3*7*7)*29*31*37*41*43*47;

unitary prime divisors: {29,31,37,41,43,47};

non-unitary prime divisors: {2,3,7}, so a(25) = 3.

MATHEMATICA

Table[Boole[n == 1] + PrimeNu@ # - Count[Transpose[FactorInteger@ #][[2]], 1] &@ CatalanNumber@ n, {n, 105}] (* Michael De Vlieger, Feb 25 2017, after Harvey P. Dale at A056169 *)

PROG

(PARI) catalan(n) = binomial(2*n, n)/(n+1);

nbud(n) = #select(x->x!=1, factor(n)[, 2]);

a(n) = nbud(catalan(n)); \\ Michel Marcus, Feb 26 2017

CROSSREFS

Cf. A000108, A034444, A048105, A056169, A056170, A080405, A081386, A081387, A081388.

Sequence in context: A226920 A123736 A185304 * A133685 A281492 A112183

Adjacent sequences:  A081386 A081387 A081388 * A081390 A081391 A081392

KEYWORD

nonn

AUTHOR

Labos Elemer, Mar 27 2003

STATUS

approved

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Last modified September 24 04:02 EDT 2020. Contains 337316 sequences. (Running on oeis4.)