A124933 Number of prime divisors (counted with multiplicity) of number of endofunctions on n points (A001372).

0, 0, 1, 1, 1, 1, 3, 3, 2, 2, 2, 2, 2, 4, 2, 3, 5, 3, 3, 3, 3, 5, 3, 2, 7, 9, 5, 3, 5, 5, 6, 3, 5, 6, 1, 2, 5, 4, 3, 4, 3, 3, 7, 7, 5, 7, 8, 4, 12, 7, 8, 1, 7, 4, 2, 4, 5, 4, 2, 5, 4, 3, 5, 6, 12, 2, 3, 5, 2, 3, 4, 4, 3, 5, 6, 2, 6, 3, 5, 3, 7, 2, 3, 7, 7, 8, 6, 5, 2, 7, 7, 4, 10, 11, 7, 7, 5, 4, 5, 6

Offset: 0

Author

Jonathan Vos Post, Nov 12 2006

Keywords

• nonn

Comments

Number of prime divisors (counted with multiplicity) of A001372 Number of mappings (or mapping patterns) from n points to themselves; number of endofunctions. {n: a(n) = 1} give the primes, beginning: A001372(2) = 3, A001372(3) = 7, A001372(4) = 19, A001372(2) = 47. {n: a(n) = 2} give the semiprimes, beginning: A001372(8) = 951 = 3 * 317, A001372(9) = 2615 = 5 * 523, A001372(10) = 7318 = 2 * 3659, A001372(11) = 20491 = 31 * 661, A001372(12) = 57903 = 3 * 19301, A001372(14) = 466199 = 107 * 4357, A001372(23) = 6218869389 = 3 * 2072956463. 3-almost primes begin: A001372(6) = 130 = 2 * 5 * 13, A001372(7) = 343 = 7^3, A001372(15) = 1328993 = 19 * 113 * 619, A001372(17) = 10884049 = 11 * 353 * 2803, A001372(18) = 31241170 = 2 * 5 * 3124117, A001372(19) = 89814958 = 2 * 5113 * 8783, A001372(20) = 258604642 = 2 * 101 * 1280221, A001372(22) = 2152118306 = 2 * 13 * 82773781, A001372(27) = 437571896993.

Links

• Harald Fripertinger and Peter Schopf, Endofunctions of given cycle type, The Annales des Sciences Mathematiques du Quebec 23 (2), 173 - 187, 1999. Web page links to PDF. Relates combinatorial species theory to more classical enumeration.

Crossrefs

Cf. A000040, A000312, A002861, A006961, A001372, A001373, A054050, A054745.

Formula

a(n) = Omega(A001372(n)) = A001222(A001372(n)).

Extensions

More terms from R. J. Mathar, Sep 23 2007