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%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
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