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A119908
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Largest squared prime factor of the odd Catalan number (A038003(n)) or 1, if it is squarefree.
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5
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1, 1, 3, 1, 11, 13, 13, 29, 43, 61, 79, 107, 181, 251, 359, 509, 719, 1021, 1447, 2039, 2887, 4093, 5717, 8179, 11579
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OFFSET
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2,3
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COMMENTS
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Odd Catalan number is A038003(n) = A000108(2^n-1) = binomial(2^(n+1)-2, 2^n-1)/(2^n).
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LINKS
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EXAMPLE
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There is no a(1) because A038003(1) = 1.
a(2) = 1 because A038003(2) = 5 which is squarefree.
a(3) = 1 because A038003(3) = 429 = 3*11*13 which is squarefree.
a(4) = 3 because A038003(4) = 9694845 = 3^2*5*17*19*23*29.
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PROG
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(Python)
from sympy import factorint
for n in range(2, 2**16):
....for p, e in factorint(4*n-2).items():
........if p in c:
............c[p] += e
........else:
............c[p] = e
....for p, e in factorint(n+1).items():
........if c[p] == e:
............del c[p]
........else:
............c[p] -= e
....if n == s:
........c2 = [p for p, e in c.items() if e >= 2]
........A119908_list.append(1 if c2 == [] else max(c2))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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