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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

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*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

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

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Last modified December 12 15:01 EST 2017. Contains 295939 sequences.