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

Author

Huen Yeong Kong (cosmology(AT)pacific.net.sg), Sep 25 2008

Keywords

• nonn

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.

Crossrefs

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

Programs

Haskell

a144925 = length . a163870_row  -- Reinhard Zumkeller, Mar 29 2014

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 *)

PARI

k=1;vector(120,n,while(isprime(k++),0);numdiv(k)-2)

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

Extensions

Sequence extended by Juri-Stepan Gerasimov, Aug 05 2009

Edited and extended by Franklin T. Adams-Watters, Aug 30 2009