%I A144925
%S A144925 1,2,2,1,2,4,2,2,3,4,4,2,2,6,1,2,2,4,6,4,2,2,2,7,2,2,6,6,4,4,2,8,1,4,
%T A144925 2,4,6,2,6,2,2,10,2,4,5,2,6,4,2,6,10,2,4,4,2,6,8,3,2,10,2,2,2,6,10,2,
%U A144925 4,2,2,2,10,4,4,7,6,6,6,2,10,6,2,8,6,2,4,4,2,2,14,1,2,2,4,2,10,6,2,6
%N A144925 Number of nontrivial divisors of the nth composite number.
%C A144925 1 and the number itself are excluded as divisors.
%C A144925 First occurrence of k: 1, 2, 9, 6, 45, 14, 24, 32, 851, 42, 3531, 148, 
               109, 89, 58993, 138, ..., ; which corresponds to the composite number 
               (A005179): 4, 6, 16, 12, 64, 24, 36, 48, 1024, 60, 4096, 192, 144, 
               120, 65536, 180, ..., . [From Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Aug 30 2009]
%D A144925 Y. K. Huen, A matrix map for prime and non-prime numbers, Int J Math. 
               Educ. Sci. Technol} 6: 913-920, 1994.
%F A144925 a(n) = A070824(A002808(n)) = A000005(A002808(n)) - 2.
%F A144925 A144925(n) = A070824(A002808(n)) = A000005(A002808(n))-2. [From Robert 
               G. Wilson v (rgwv(AT)rgwv.com), Aug 30 2009]
%t A144925 Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n 
               + 1]; f[n_] := DivisorSigma[0, n] - 2; Table[f@ Composite@ n, {n, 
               101}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 30 2009]
%o A144925 (PARI) k=1;vector(120,n,while(isprime(k++),0);numdiv(k)-2)
%Y A144925 Cf. A002808, A000005, A070824, A005179. [From Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Aug 30 2009]
%Y A144925 Sequence in context: A055076 A069780 A066954 this_sequence A029262 A129687 
               A128176
%Y A144925 Adjacent sequences: A144922 A144923 A144924 this_sequence A144926 A144927 
               A144928
%K A144925 nonn
%O A144925 1,2
%A A144925 Huen Yeong Kong (cosmology(AT)pacific.net.sg), Sep 25 2008
%E A144925 Sequence extended by Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 
               05 2009
%E A144925 Edited and extended by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Aug 30 2009