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A001014
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6th powers: a(n) = n^6.
(Formerly M5330 N2318)
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27
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0, 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000, 1771561, 2985984, 4826809, 7529536, 11390625, 16777216, 24137569, 34012224, 47045881, 64000000, 85766121, 113379904, 148035889, 191102976, 244140625, 308915776
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Numbers both square and cubic - pdg(AT)worldofnumbers.com.
Totally multiplicative sequence with a(p) = p^6 for prime p. [From Jaroslav Krizek, Nov 01 2009]
Numbers n for which order of torsion subgroup t of the elliptic curve y^2=x^3+n is t=6. [From Artur Jasinski, Jun 30 2010]
Besides the first term this sequence is the denominator of ((pi)^6)/945=1+1/64+1/729+1/4096+1/15625+1/46656+... - Mohammad K. Azarian, Nov 01 2011
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REFERENCES
| Granino A. Korn and Theresa M.Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968), p. 982 [From Mohammad K. Azarian, November 1 2011].
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Franklin T. Adams-Watters, Table of n, a(n) for n = 0..500
Henry Bottomley, Illustration of initial terms
Gebel J., Integer points on Mordell curves [From Artur Jasinski (grafix(AT)csl.pl), Jun 30 2010]
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| Multiplicative with a(p^e) = p^(6e). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
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MAPLE
| a:=n->sum(sum(n^4, j=1..n), k=1..n): seq(a(n), n=0..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
A001014:=-(z+1)*(z**4+56*z**3+246*z**2+56*z+1)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
{seq( i^3, i = 0..15900)} intersect {seq(k^2, k= 0..15900)} ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2008
with(finance):seq(add(growingperpetuity(n^5, 2, 1), k=1..n), n=0..26); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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MATHEMATICA
| Table[n^6, {n, 0, 40}] (* Vladimir Orlovsky, Feb 19 2010 *)
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PROG
| (Haskell)
a001014 n = a001014_list !! n
a001014_list = map (^ 6) [0..] -- Reinhard Zumkeller, Dec 04 2011
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CROSSREFS
| a(n) = A123866(n) + 1.
Subsequence of A201217.
Cf. A000540 (partial sums).
Sequence in context: A016899 A017676 A055015 * A050753 A074154 A153160
Adjacent sequences: A001011 A001012 A001013 * A001015 A001016 A001017
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KEYWORD
| nonn,easy,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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