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Search: id:A164577
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| A164577 |
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Integer averages of the first perfect cubes up to some n^3. |
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+0
4
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| 1, 12, 25, 45, 112, 162, 225, 396, 507, 637, 960, 1156, 1377, 1900, 2205, 2541, 3312, 3750, 4225, 5292, 5887, 6525, 7936, 8712, 9537, 11340, 12321, 13357, 15600, 16810, 18081, 20812, 22275, 23805, 27072, 28812, 30625, 34476, 36517, 38637, 43120
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Integers of the form A000537(k)/k, created by the k>0 listed in A042965. [R. J. Mathar, Aug 20 2009]
Also, integers of the form (1/4)*n*(n+1)^2 for some n. [From Zak Seidov (zakseidov(AT)yahoo.com), Aug 17 2009]
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EXAMPLE
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The average of the first cube is 1^3/1=1=a(1).
The average of the first two cubes is (1^3+2^3)/2=9/2, not integer, and does not contribute to the sequence.
The average of the first three cubes is (1^3+2^3+3^3)/3=12, integer, and defines a(2).
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MATHEMATICA
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Timing[s=0; lst={}; Do[a=(s+=n^3)/n; If[Mod[a, 1]==0, AppendTo[lst, a]], {n, 5!}]; lst]
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CROSSREFS
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Cf. A050248, A051456, A078617, A078618, A154293, A164576
Sequence in context: A042851 A041280 A132754 this_sequence A058848 A042869 A041282
Adjacent sequences: A164574 A164575 A164576 this_sequence A164578 A164579 A164580
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KEYWORD
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nonn,easy
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 16 2009
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EXTENSIONS
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Changed comments to examples - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 20 2009
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