

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
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OFFSET

2,3


COMMENTS

Odd Catalan number is A038003(n) = A000108(2^n1) = binomial(2^(n+1)2, 2^n1)/(2^n).


LINKS

Table of n, a(n) for n=2..26.


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*n2).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

Cf. A038003, A000108.
Sequence in context: A008969 A199577 A228534 * A153257 A002185 A002589
Adjacent sequences: A119905 A119906 A119907 * A119909 A119910 A119911


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Aug 02 2006


EXTENSIONS

a(16)a(26) from Chai Wah Wu, Feb 12 2015


STATUS

approved



