A119908 Largest squared prime factor of the odd Catalan number (A038003(n)) or 1, if it is squarefree.

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

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 * A362996 A153257 A002185

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