cp's OEIS Frontend

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

%I A119908 #12 Feb 12 2025 19:02:43
%S A119908 1,1,3,1,11,13,13,29,43,61,79,107,181,251,359,509,719,1021,1447,2039,
%T A119908 2887,4093,5717,8179,11579
%N A119908 Largest squared prime factor of the odd Catalan number (A038003(n)) or 1, if it is squarefree.
%C A119908 Odd Catalan number is A038003(n) = A000108(2^n-1) = binomial(2^(n+1)-2, 2^n-1)/(2^n).
%e A119908 There is no a(1) because A038003(1) = 1.
%e A119908 a(2) = 1 because A038003(2) = 5 which is squarefree.
%e A119908 a(3) = 1 because A038003(3) = 429 = 3*11*13 which is squarefree.
%e A119908 a(4) = 3 because A038003(4) = 9694845 = 3^2*5*17*19*23*29.
%o A119908 (Python)
%o A119908 from sympy import factorint
%o A119908 A119908_list, c, s = [], {}, 3
%o A119908 for n in range(2, 2**16):
%o A119908     for p, e in factorint(4*n-2).items():
%o A119908         if p in c:
%o A119908             c[p] += e
%o A119908         else:
%o A119908             c[p] = e
%o A119908     for p, e in factorint(n+1).items():
%o A119908         if c[p] == e:
%o A119908             del c[p]
%o A119908         else:
%o A119908             c[p] -= e
%o A119908     if n == s:
%o A119908         c2 = [p for p, e in c.items() if e >= 2]
%o A119908         A119908_list.append(1 if c2 == [] else max(c2))
%o A119908         s = 2*s+1 # _Chai Wah Wu_, Feb 12 2015
%Y A119908 Cf. A038003, A000108.
%K A119908 nonn
%O A119908 2,3
%A A119908 _Alexander Adamchuk_, Aug 02 2006
%E A119908 a(16)-a(26) from _Chai Wah Wu_, Feb 12 2015