

A023052


Powerful numbers (3): numbers n that are the sum of some fixed power of their digits.


27



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
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OFFSET

1,3


COMMENTS

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). [R. J. Mathar, Jun 15 2009, Jun 22 2009]


LINKS

Joseph Myers, Table of n, a(n) for n=1..255
Hans Havermann, Extended table of values for A023052 and A046074
J. Randle, Powerful numbers, Note 3208, Math. Gaz. 52 (1968), 383.
Eric Weisstein's World of Mathematics, Narcissistic Number
Index entries for sequences related to powerful numbers


EXAMPLE

153 = 1^3 + 5^3 + 3^3, 4210818 = 4^7 + 2^7 + 1^7 + 0^7 + 8^7 + 1^7 + 8^7.


CROSSREFS

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 * A005188 A032569 A039723
Adjacent sequences: A023049 A023050 A023051 * A023053 A023054 A023055


KEYWORD

nonn,base,nice,changed


AUTHOR

David W. Wilson


EXTENSIONS

Computed to 10^50 by G. N. Gusev (GGN(AT)rm.yaroslavl.ru)
Computed to 10^74 by Xiaoqing Tang
Anumber typo corrected by R. J. Mathar, Jun 22 2009
Computed to 10^105 by Joseph Myers
Crossreferences edited by Joseph Myers, Jun 28 2009


STATUS

approved



