A144925 Number of nontrivial divisors of the n-th composite number.

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

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

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

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

Sequence in context: A354825 A210531 A066954 * A029262 A363825 A368470

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