login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A030078 Cubes of primes. 78
8, 27, 125, 343, 1331, 2197, 4913, 6859, 12167, 24389, 29791, 50653, 68921, 79507, 103823, 148877, 205379, 226981, 300763, 357911, 389017, 493039, 571787, 704969, 912673, 1030301, 1092727, 1225043, 1295029, 1442897, 2048383, 2248091, 2571353, 2685619 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers with exactly three factorizations: A001055(a(n)) = 3 (e.g., a(4) = 1*343 = 7*49 = 7*7*7). - Reinhard Zumkeller, Dec 29 2001

Solutions of the equation n'=3*n^(2/3), where n' is the arithmetic derivative of n. - Paolo P. Lava, Oct 31 2012

Intersection of A014612 and A000578. Intersection of A014612 and A030513. - Wesley Ivan Hurt, Sep 10 2013

REFERENCES

E. Landau, Elementary Number Theory, translation by Jacob E. Goodman of Elementare Zahlentheorie (Vol. I_1 (1927) of Vorlesungen ueber Zahlentheorie), by Edmund Landau, with added exercises by Paul T. Bateman and E. E. Kohlbecker, Chelsea Publishing Co., New York, 1958, pp. 31-32.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, MathWorld: Prime Power

FORMULA

n such that A062799(n) = 3. - Benoit Cloitre, Apr 06 2002

a(n) = A000040(n)^3. - Omar E. Pol, Jul 27 2009]

A064380(a(n)) = A000010(a(n)). - Vladimir Shevelev, Apr 19 2010

A003415(a(n)) = A079705(n). - Reinhard Zumkeller, Jun 26 2011

A056595(a(n)) = 2. - Reinhard Zumkeller, Aug 15 2011

A000005(a(n)) = 4. - Wesley Ivan Hurt, Sep 10 2013

EXAMPLE

a(3) = 125; since the 3rd prime is 5, a(3) = 5^3 = 125.

MATHEMATICA

Array[Prime[ # ]^3&, 5! ] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)

PROG

(Sage) BB = primes_first_n(36) list = [] for i in range(36): list.append(BB[i]^3) list # Zerinvary Lajos, May 15 2007

(Haskell)

a030078 = a000578 . a000040

a030078_list = map a000578 a000040_list -- Reinhard Zumkeller, May 26 2012

(PARI) a(n)=prime(n)^3 \\ Charles R Greathouse IV, Mar 20 2013

(MAGMA) [p^3: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014

CROSSREFS

Cf. A001248, A060800, A131991, A000040, A001248, A000578, subsequence of A046099.

Subsequence of A007422.

Sequence in context: A062838 A240859 A046452 * A051751 A133042 A181361

Adjacent sequences:  A030075 A030076 A030077 * A030079 A030080 A030081

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 27 04:47 EST 2014. Contains 250155 sequences.