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).

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, 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, 2, 3, 4, 1, 3, 2, 2, 1, 2, 3

Offset

1,3

Links

Table of n, a(n) for n=1..78.

Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, Handbook of Applied Cryptography, CRC Press, ISBN: 0-8493-8523-7, October 1996, 816 pages, 5th printing, August 2001.

Formula

a(n) = bigomega(A073726(n)) = Omega(A073726(n)) = A001222(A073726(n)).

Example

a(48) = 4 because A073726(48) = 100, and Omega(100 = 2^2 * 5^2) = 4.

Crossrefs

Cf. A001222, A073726, See A074744 for corresponding values of k.

Sequence in context: A165413 A172155 A080573 * A006340 A270641 A076371

Adjacent sequences: A186437 A186438 A186439 * A186441 A186442 A186443

Keyword

nonn,easy

Author

Jonathan Vos Post, Feb 21 2011

Extensions

a(49) - a(78) from Nathaniel Johnston, Apr 26 2011

Status

approved