cp's OEIS Frontend

A186440 Number of prime divisors (counted with multiplicity) of n such that the primitive irreducible trinomial x^n + x^k + 1 is a primitive irreducible polynomial (mod 2) for some k with 0 < k < n (A073726).

%I A186440 #8 Mar 31 2012 13:22:29
%S A186440 1,1,2,1,2,1,2,2,1,2,1,3,3,2,2,1,2,3,1,1,2,2,4,2,1,1,2,3,2,2,2,4,3,2,
%T A186440 3,1,1,1,4,4,2,1,2,2,2,1,3,4,1,3,2,5,2,1,2,2,2,2,3,1,2,3,4,2,4,1,4,2,
%U A186440 2,3,4,1,3,2,2,1,2,3
%N A186440 Number of prime divisors (counted with multiplicity) of n such that the primitive irreducible trinomial x^n + x^k + 1 is a primitive irreducible polynomial (mod 2) for some k with 0 < k < n (A073726).
%H A186440 Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, <a href="http://www.cacr.math.uwaterloo.ca/hac/">Handbook of Applied Cryptography</a>, CRC Press, ISBN: 0-8493-8523-7, October 1996, 816 pages, 5th printing, August 2001.
%F A186440 a(n) = bigomega(A073726(n)) = Omega(A073726(n)) = A001222(A073726(n)).
%e A186440 a(48) = 4 because A073726(48) = 100, and Omega(100 = 2^2 * 5^2) = 4.
%Y A186440 Cf. A001222, A073726, See A074744 for corresponding values of k.
%K A186440 nonn,easy
%O A186440 1,3
%A A186440 _Jonathan Vos Post_, Feb 21 2011
%E A186440 a(49) - a(78) from _Nathaniel Johnston_, Apr 26 2011