A240978 - OEIS

%I #29 Aug 19 2014 01:07:44

%S 2,2,7,31,127,73,691,8191,3617,131071,524287,593,2294797,657931,

%T 362903,1001259881,2147483647,151628697551,26315271553053477373,

%U 154210205991661,1897170067619,1520097643918070802691,1798482437,67568238839737,153289748932447906241

%N The largest prime divisor of A246053(n).

%C According to theorem 2 of the Milnor paper a(2) and a(4) through a(8) are lower bounds for the number of distinct differentiable structures on spheres S^(4*k-1) for k = 2 and 4,..,8. Better bounds are given in A242032.

%H John Milnor, <a href="http://www.jstor.org/stable/2372998">Differentiable Structures on Spheres</a>, American Journal of Mathematics, Vol. 81, No. 4 (Oct., 1959), pp. 962-972. [See p. 971]

%F a(n) = A006530(A246053(n)). - _Michel Marcus_, Aug 18 2014

%o (Sage)

%o h = lambda x: zeta(2*x)*(4^x-2)

%o A246053 = lambda n: Integer((h((n+1)//2)*h(n//2)/h(n)).denominator())

%o A240978 = lambda n: max(prime_divisors(A246053(n)))

%o [A240978(n) for n in range(25)]

%Y Cf. A246053, A246052, A242032.

%K nonn

%O 0,1

%A _Peter Luschny_, Aug 12 2014