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 A030078 Cubes of primes. 127
 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. Cf. A036966, A258600. Sequence in context: A240859 A277047 A046452 * A051751 A133042 A181361 Adjacent sequences:  A030075 A030076 A030077 * A030079 A030080 A030081 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified August 15 09:12 EDT 2018. Contains 313756 sequences. (Running on oeis4.)