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%I #19 Nov 15 2018 09:30:19
%S 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 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 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 Number of nontrivial divisors of the n-th composite number.
%C 1 and the number itself are excluded as divisors.
%C 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, ..., . - _Robert G. Wilson v_, Aug 30 2009
%C Row lengths of table in A163870. - _Reinhard Zumkeller_, Mar 29 2014
%H Reinhard Zumkeller, <a href="/A144925/b144925.txt">Table of n, a(n) for n = 1..10000</a>
%H R. P. Boas & N. J. A. Sloane, <a href="/A005381/a005381.pdf">Correspondence, 1974</a>
%H Y. K. Huen, <a href="http://www.tandfonline.com/doi/ref/10.1080/0020739940250616">A matrix map for prime and non-prime numbers</a>, Int J Math. Educ. Sci. Technol. 6: 913-920, 1994.
%F a(n) = A070824(A002808(n)) = A000005(A002808(n)) - 2.
%F A144925(n) = A070824(A002808(n)) = A000005(A002808(n)) - 2. - _Robert G. Wilson v_, Aug 30 2009
%t Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n + 1]; f[n_] := DivisorSigma[0, n] - 2; Table[f@ Composite@ n, {n, 101}] (* _Robert G. Wilson v_, Aug 30 2009 *)
%t DivisorSigma[0,#]-2&/@Select[Range[300],CompositeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 15 2018 *)
%o (PARI) k=1;vector(120,n,while(isprime(k++),0);numdiv(k)-2)
%o (Haskell)
%o a144925 = length . a163870_row -- _Reinhard Zumkeller_, Mar 29 2014
%Y Cf. A002808, A000005, A070824, A005179. - _Robert G. Wilson v_, Aug 30 2009
%K nonn
%O 1,2
%A Huen Yeong Kong (cosmology(AT)pacific.net.sg), Sep 25 2008
%E Sequence extended by _Juri-Stepan Gerasimov_, Aug 05 2009
%E Edited and extended by _Franklin T. Adams-Watters_, Aug 30 2009
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