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Search: id:A023052
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| A023052 |
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Powerful numbers (3): numbers n that are the sum of some fixed power of their digits. |
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+0
23
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| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 4150, 4151, 8208, 9474, 54748, 92727, 93084, 194979, 548834, 1741725, 4210818, 9800817, 9926315, 14459929, 24678050, 24678051, 88593477, 146511208, 472335975, 534494836, 912985153
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Let n = d_1 d_2 ... d_k in base 10; then n = Sum_{i=1..k} d_i^s for some s.
Superset of A005188, A046197 (s=3), A052455 (s=4), A052464 (s=5), A124068 (s=6,7), A124069 (s=8). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2009, Jun 22 2009]
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REFERENCES
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J. Randle, Powerful numbers, Note 3208, Math. Gaz. 52 (1968), 383.
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LINKS
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Joseph Myers, Table of n, a(n) for n=1..255
Index entries for sequences related to powerful numbers
Hans Havermann, Extended table of values for A023052 and A046074
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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153 = 1^3 + 5^3 + 3^3, 4210818 = 4^7 + 2^7 + 1^7 + 0^7 + 8^7 + 1^7 + 8^7.
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CROSSREFS
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Cf. A001694, A007532, A005934, A003321, A014576, A046074, A046761, A053540, A161752.
Similar to but different from A005188.
In other bases: A162216 (base 3), A162219 (base 4), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162231 (base 8), A162234 (base 9).
Sequence in context: A001104 A151544 A032561 this_sequence A005188 A032569 A039723
Adjacent sequences: A023049 A023050 A023051 this_sequence A023053 A023054 A023055
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KEYWORD
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nonn,base,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Computed to 10^50 by G. N. Gusev (GGN(AT)rm.yaroslavl.ru)
Computed to 10^74 by Xiaoqing Tang
A-number typo corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 22 2009
Computed to 10^105 by Joseph Myers
Cross-references edited by Joseph Myers (jsm(AT)polyomino.org.uk), Jun 28 2009
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