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A001015
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Seventh powers: a(n) = n^7.
(Formerly M5392 N2341)
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10
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0, 1, 128, 2187, 16384, 78125, 279936, 823543, 2097152, 4782969, 10000000, 19487171, 35831808, 62748517, 105413504, 170859375, 268435456, 410338673, 612220032, 893871739, 1280000000, 1801088541, 2494357888, 3404825447
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Totally multiplicative sequence with a(p) = p^7 for prime p. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009]
For n>0, (a(3*n-1)^7-a(2*n-1)^7-a(n)^7)/(7*(3*n-1)*(2*n-1)*n) = (2*A001106(n)+1)^2 (see Barisien reference, problem 173). - Bruno Berselli, Feb 01 2011
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REFERENCES
| 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).
E.-N. Barisien, Supplemento al Periodico di Matematica, Raffaello Giusti Editore (Livorno), July 1913, p. 135 (Problem 173).
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LINKS
| 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.
Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
| Multiplicative with a(p^e) = p^(7e). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
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MAPLE
| A001015:=z*(1191*z^4+120*z^5+1191*z^2+2416*z^3+120*z+z^6+1)/(z-1)^8; [S. Plouffe in his 1992 dissertation], offset corrected by M. F. Hasler, Feb 01 2011
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MATHEMATICA
| Table[n^7, {n, 0, 40}] (* From Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
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CROSSREFS
| Cf. A000584.
Sequence in context: A195594 A017678 A123253 * A050754 A113852 A046456
Adjacent sequences: A001012 A001013 A001014 * A001016 A001017 A001018
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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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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000
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