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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A095370 Number of distinct prime factors of the repunit (-1 + 10^n)/9. 15
0, 1, 2, 2, 2, 5, 2, 4, 3, 4, 2, 7, 3, 4, 6, 6, 2, 8, 1, 7, 7, 6, 1, 10, 5, 6, 5, 8, 5, 13, 3, 11, 6, 6, 7, 11, 3, 3, 6, 11, 4, 14, 4, 10, 9, 6, 2, 13, 4, 10, 8, 9, 4, 12, 8, 12, 6, 8, 2, 20, 7, 5, 13, 15, 7, 14, 3, 10, 6, 12, 2, 17, 3, 7, 12, 6, 8, 15, 6, 15, 10, 7, 3, 21, 7, 8, 10, 14, 5, 21, 12, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Factoring certain repunits is especially difficult.

REFERENCES

Yates, S. "Peculiar Properties of Repunits." J. Recr. Math. 2, 139-146,1969.

Yates, S. "Prime Divisors of Repunits." J. Recr. Math. 8, 33-38, 1975.

LINKS

Ray Chandler, Table of n, a(n) for n = 1..322

P. De Geest, Repunits and their prime factors

T. Granlund, Repunits.

M. Kamada, Factorization of 11...11(Repunits)

Y. Koide, Factorization of Repunit Numbers

W. M. Snyder, Factoring Repunits, Am. Math. Monthly 89, 462-466, 1982.

P. Yiu, Factorizations of repunits R_n for n<=50 Appendix Chap.18.5 pp. 173/360 in 'Recreational Mathematics'

FORMULA

a(n) = A001221(A002275(n)).

EXAMPLE

a(62)=5 because

11111111111111111111111111111111111111111111111111111111111111 =

11 * 2791 * 6943319 * 57336415063790604359 * 909090909090909090909090909091.

a(97)=3 because (10^97 - 1)/9 = 12004721 * 846035731396919233767211537899097169 * 109399846855370537540339266842070119107662296580348039.

MATHEMATICA

lst={}; Do[p=(10^n-1)/9; AppendTo[lst, Length[FactorInteger[p]]], {n, 0, 2*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 15 2009 *)

PROG

(PARI) a(n)=omega(10^n\9) \\ Charles R Greathouse IV, Sep 14 2015

CROSSREFS

Cf. A067063, A003020, A001221, A002275, A095371.

Cf. A046053 (total number of prime factors).

Sequence in context: A183413 A183380 A260587 * A046053 A080348 A096396

Adjacent sequences:  A095367 A095368 A095369 * A095371 A095372 A095373

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 04 2004; corrected Jun 09 2004

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 March 4 20:38 EST 2021. Contains 341803 sequences. (Running on oeis4.)