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A119908 Largest squared prime factor of the odd Catalan number (A038003(n)) or 1, if it is squarefree. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
COMMENTS
Odd Catalan number is A038003(n) = A000108(2^n-1) = binomial(2^(n+1)-2, 2^n-1)/(2^n).
LINKS
EXAMPLE
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.
PROG
(Python)
from sympy import factorint
A119908_list, c, s = [], {}, 3
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))
........s = 2*s+1 # Chai Wah Wu, Feb 12 2015
CROSSREFS
Sequence in context: A008969 A199577 A228534 * A362996 A153257 A002185
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Aug 02 2006
EXTENSIONS
a(16)-a(26) from Chai Wah Wu, Feb 12 2015
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)