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A144925
Number of nontrivial divisors of the n-th composite number.
9
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
OFFSET
1,2
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, ..., . - Robert G. Wilson v, Aug 30 2009
Row lengths of table in A163870. - Reinhard Zumkeller, Mar 29 2014
LINKS
R. P. Boas & N. J. A. Sloane, Correspondence, 1974
Y. K. Huen, A matrix map for prime and non-prime numbers, Int J Math. Educ. Sci. Technol. 6: 913-920, 1994.
FORMULA
a(n) = A070824(A002808(n)) = A000005(A002808(n)) - 2.
A144925(n) = A070824(A002808(n)) = A000005(A002808(n)) - 2. - Robert G. Wilson v, Aug 30 2009
MATHEMATICA
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 *)
DivisorSigma[0, #]-2&/@Select[Range[300], CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 15 2018 *)
PROG
(PARI) k=1; vector(120, n, while(isprime(k++), 0); numdiv(k)-2)
(Haskell)
a144925 = length . a163870_row -- Reinhard Zumkeller, Mar 29 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Huen Yeong Kong (cosmology(AT)pacific.net.sg), Sep 25 2008
EXTENSIONS
Sequence extended by Juri-Stepan Gerasimov, Aug 05 2009
Edited and extended by Franklin T. Adams-Watters, Aug 30 2009
STATUS
approved