|
Search: id:A000584
|
|
|
| A000584 |
|
5th powers: a(n) = n^5.
(Formerly M5231 N2277)
|
|
+0
52
|
|
| 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; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Totally multiplicative sequence with a(p) = p^5 for prime p. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 01 2009]
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
|
|
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.
|
|
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
|
|
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.]
|
|
PROGRAM
|
(Other) sage: [log(e^(n^5))for n in xrange(0, 30)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
|
|
CROSSREFS
|
Partial sums give A000539.
Cf. A000012, A001477, A000290, A000578, A000583, A000539, A062392.
Sequence in context: A104782 A017674 A055014 this_sequence A050752 A153159 A113850
Adjacent sequences: A000581 A000582 A000583 this_sequence A000585 A000586 A000587
|
|
KEYWORD
|
nonn,easy,mult,new
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
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
|
|
|
Search completed in 0.003 seconds
|
