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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 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

Y. K. Huen, A matrix map for prime and non-prime numbers, Int J Math. Educ. Sci. Technol} 6: 913-920, 1994.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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 *)

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

Cf. A002808, A000005, A070824, A005179. - Robert G. Wilson v, Aug 30 2009

Sequence in context: A069780 A210531 A066954 * A029262 A193292 A275297

Adjacent sequences:  A144922 A144923 A144924 * A144926 A144927 A144928

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

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Last modified March 29 13:14 EDT 2017. Contains 284270 sequences.