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A081389
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Number of non-unitary prime divisors of Catalan numbers, i.e., number of those prime factors whose exponent is greater than one.
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6
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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
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OFFSET
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1,13
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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PROG
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(PARI) catalan(n) = binomial(2*n, n)/(n+1);
nbud(n) = #select(x->x!=1, factor(n)[, 2]);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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