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A023052 Powerful numbers (3): numbers n that are the sum of some fixed power of their digits. 29
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; refs; listen; history; text; internal format)
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]

If a term x is a multiple of 10, then x+1 is a term too. [Paolo P. Lava, Apr 07 2016]

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.

J. Randle, Powerful numbers, Note 3208, Math. Gaz. 52 (1968), 383. [Annotated scanned copy]

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.

MAPLE

P:=proc(q) local a, b, c, k, n, ok; for n from 1 to q do a:=[]; b:=n; ok:=0;

for k from 1 to ilog10(n)+1 do if (b mod 10)>1 then ok:=1; fi;

a:=[(b mod 10), op(a)]; b:=trunc(b/10); od; b:=0; c:=0;

if ok=1 then while c<n do b:=b+1; c:=add(a[k]^b, k=1..nops(a)); od;  if

c=n then print(n); fi; fi; od; end: P(10^9); # Paolo P. Lava, Feb 08 2016

MATHEMATICA

Select[Range[0, 10^5], Function[m, AnyTrue[Function[k, Total@ Map[Power[#, k] &, IntegerDigits@ m]] /@ Range@ 10, # == m &]]] (* Michael De Vlieger, Feb 08 2016, Version 10 *)

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 A254960

Adjacent sequences:  A023049 A023050 A023051 * A023053 A023054 A023055

KEYWORD

nonn,base,nice

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

A-number typo corrected by R. J. Mathar, Jun 22 2009

Computed to 10^105 by Joseph Myers

Cross-references edited by Joseph Myers, Jun 28 2009

STATUS

approved

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Last modified September 29 14:29 EDT 2016. Contains 276614 sequences.