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

Author

Alexander Adamchuk, Aug 02 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A038003, A000108.

Programs

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

Extensions

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