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A000584
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5th powers: a(n) = n^5.
(Formerly M5231 N2277)
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55
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0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, 161051, 248832, 371293, 537824, 759375, 1048576, 1419857, 1889568, 2476099, 3200000, 4084101, 5153632, 6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149
(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^5 for prime p. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009]
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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).
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LINKS
| Franklin T. Adams-Watters, Table of n, a(n) for n = 0..500
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^(5e). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
a(n) = {least common multiple of n and (n-1)^4}-(n-1)^4. E.g.: {least common multiple of 1 and (1-1)^4}-(1-1)^4 = 0, {least common multiple of 2 and (2-1)^4}-(2-1)^4 = 1, {least common multiple of 3 and (3-1)^4}-(3-1)^4 = 32, {least common multiple of 4 and (4-1)^4}-(4-1)^4 = 243, ... - Mats Granvik (mgranvik(AT)abo.fi), Sep 24 2007
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MAPLE
| a:=n->sum(sum(n^3, j=1..n), k=1..n): seq(a(n), n=0..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
A000584:=(1+26*z+66*z**2+26*z**3+z**4)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Range[0, 50]^5 (*From Vladimir Joseph Stephan Orlovsky, Feb 20 2011*)
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PROG
| (Other) sage: [log(e^(n^5))for n in xrange(0, 30)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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CROSSREFS
| Partial sums give A000539.
Cf. A000012, A001477, A000290, A000578, A000583, A000539, A062392.
Cf. A162624 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), May 27 2010]
Sequence in context: A017674 A184979 A055014 * A050752 A153159 A113850
Adjacent sequences: A000581 A000582 A000583 * A000585 A000586 A000587
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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 Henry Bottomley (se16(AT)btinternet.com), Jun 21 2001
More terms from Mats Granvik (mgranvik(AT)abo.fi), Sep 24 2007
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