login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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: A347089 A210531 A066954 * A029262 A295878 A294931

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)