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A030078
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Cubes of primes.
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58
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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
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OFFSET
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1,1
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COMMENTS
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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]
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, MathWorld: Prime Power
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FORMULA
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n such that A062799(n)=3 - Benoit Cloitre, Apr 06 2002
a(n) = A000040(n)^3. [From Omar E. Pol, Jul 27 2009]
A064380(a(n))=A000010(a(n)) [From Vladimir Shevelev, Apr 19 2010]
A003415(a(n)) = A079705(n). [Reinhard Zumkeller, Jun 26 2011]
A056595(a(n)) = 2. [Reinhard Zumkeller, Aug 15 2011]
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MATHEMATICA
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Array[Prime[ # ]^3&, 5! ] [From Vladimir Orlovsky, Sep 01 2008]
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PROG
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(SAGE) BB = primes_first_n(36) list = [] for i in range(36): list.append(BB[i]^3) list - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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
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CROSSREFS
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Cf. A001248, A060800, A131991, A000040, A001248, A000578, subsequence of A046099.
Sequence in context: A153147 A062838 A046452 * A051751 A133042 A181361
Adjacent sequences: A030075 A030076 A030077 * A030079 A030080 A030081
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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