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A144925
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Number of nontrivial divisors of the n-th composite number.
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4
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 1 and the number itself are excluded as divisors.
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]
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REFERENCES
| Y. K. Huen, A matrix map for prime and non-prime numbers, Int J Math. Educ. Sci. Technol} 6: 913-920, 1994.
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FORMULA
| a(n) = A070824(A002808(n)) = A000005(A002808(n)) - 2.
A144925(n) = A070824(A002808(n)) = A000005(A002808(n))-2. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 30 2009]
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MATHEMATICA
| 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]
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PROG
| (PARI) k=1; vector(120, n, while(isprime(k++), 0); numdiv(k)-2)
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CROSSREFS
| Cf. A002808, A000005, A070824, A005179. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 30 2009]
Sequence in context: A055076 A069780 A066954 * A029262 A193292 A129687
Adjacent sequences: A144922 A144923 A144924 * A144926 A144927 A144928
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KEYWORD
| nonn
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AUTHOR
| Huen Yeong Kong (cosmology(AT)pacific.net.sg), Sep 25 2008
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EXTENSIONS
| Sequence extended by Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 05 2009
Edited and extended by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 30 2009
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