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

%I A124933 #6 Mar 30 2012 18:40:41
%S A124933 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,
%T A124933 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,
%U A124933 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
%N A124933 Number of prime divisors (counted with multiplicity) of number of endofunctions on n points (A001372).
%C A124933 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.
%H A124933 Harald Fripertinger and Peter Schopf, <a href="http://www.uni-graz.at/~fripert/endofunctions.html">Endofunctions of given cycle type</a>, 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.
%F A124933 a(n) = Omega(A001372(n)) = A001222(A001372(n)).
%Y A124933 Cf. A000040, A000312, A002861, A006961, A001372, A001373, A054050, A054745.
%K A124933 nonn
%O A124933 0,7
%A A124933 _Jonathan Vos Post_, Nov 12 2006
%E A124933 More terms from _R. J. Mathar_, Sep 23 2007