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Search: id:A048798
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| A048798 |
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Smallest number k (k>0) such that nk is a perfect cube. |
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+0
7
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| 1, 4, 9, 2, 25, 36, 49, 1, 3, 100, 121, 18, 169, 196, 225, 4, 289, 12, 361, 50, 441, 484, 529, 9, 5, 676, 1, 98, 841, 900, 961, 2, 1089, 1156, 1225, 6, 1369, 1444, 1521, 25, 1681, 1764, 1849, 242, 75, 2116, 2209, 36, 7, 20, 2601, 338, 2809, 4, 3025, 49, 3249
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Smarandache complementary cubic function.
Note that in general the smallest number k(>0) such that nk is a perfect mth-power (rather obviously) =(the smallest mth-power divisible by n)/n, and also (slightly less obviously) =n^(m-1)/(the number of solutions of x^m==0 mod n)^m
Multiplicative with a(p^e) = p^(2 - e%3). Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) May 17, 2005.
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REFERENCES
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K. Atanassov, On the 22-nd, the 23-rd, and 24-th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1998), No. 2, 80-82.
K. Atanassov, On Some of Smarandache's Problems, American Research Press, 1999, 16-21.
F. Smarandache, Only Problems not Solutions!, Xiquan Publ. Hse., 1993.
M. Popescu, M. Nicolescu, About the Smarandache Complementary Cubic Function, Smarandache Notions Journal, Vol. 7, No. 1-2-3, 1996, 54-62.
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LINKS
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K. Atanassov, On Some of Smarandache's Problems
H. Bottomley, Some Smarandache-type multiplicative sequences
M. L. Perez et al., eds., Smarandache Notions Journal
F. Smarandache, Only Problems, Not Solutions!
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FORMULA
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a(n) = A053149(n)/n = n^2/A000189(n)^3.
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EXAMPLE
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a(12)=18 because 18 is the smallest number such that 12*18 is a perfect cube. a(28)=a(2*2*7)=2*7*7=98 since 28*98=(14)^3.
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CROSSREFS
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Cf. A007913.
Sequence in context: A114578 A135044 A064505 this_sequence A007914 A048758 A011262
Adjacent sequences: A048795 A048796 A048797 this_sequence A048799 A048800 A048801
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Charles T. Le (charlestle(AT)yahoo.com)
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EXTENSIONS
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More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Feb 15 2000. Comments from Henry Bottomley (se16(AT)btinternet.com), Mar 03 2000
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