A119908 - OEIS

%I #9 Feb 13 2015 09:32:18

%S 1,1,3,1,11,13,13,29,43,61,79,107,181,251,359,509,719,1021,1447,2039,

%T 2887,4093,5717,8179,11579

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

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

%e There is no a(1) because A038003(1) = 1.

%e a(2) = 1 because A038003(2) = 5 which is squarefree.

%e a(3) = 1 because A038003(3) = 429 = 3*11*13 which is squarefree.

%e a(4) = 3 because A038003(4) = 9694845 = 3^2*5*17*19*23*29.

%o (Python)

%o from sympy import factorint

%o A119908_list, c, s = [], {}, 3

%o for n in range(2,2**16):

%o ....for p,e in factorint(4*n-2).items():

%o ........if p in c:

%o ............c[p] += e

%o ........else:

%o ............c[p] = e

%o ....for p,e in factorint(n+1).items():

%o ........if c[p] == e:

%o ............del c[p]

%o ........else:

%o ............c[p] -= e

%o ....if n == s:

%o ........c2 = [p for p,e in c.items() if e >= 2]

%o ........A119908_list.append(1 if c2 == [] else max(c2))

%o ........s = 2*s+1 # _Chai Wah Wu_, Feb 12 2015

%Y Cf. A038003, A000108.

%K nonn

%O 2,3

%A _Alexander Adamchuk_, Aug 02 2006

%E a(16)-a(26) from _Chai Wah Wu_, Feb 12 2015