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A007532 Powerful numbers (2): a sum of positive powers of its digits.
(Formerly M0487)
16
1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 43, 63, 89, 132, 135, 153, 175, 209, 224, 226, 262, 264, 267, 283, 332, 333, 334, 357, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 407, 445, 463, 518, 598, 629, 739, 794, 849, 935, 994, 1034 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

David W. Wilson, Table of n, a(n) for n = 1..10000

Giovanni Resta, d-Powerful numbers the 30067 terms and sums up to 10^6.

Eric Weisstein's World of Mathematics, Powerful Number.

Index entries for sequences related to powerful numbers

FORMULA

If n = d_1 d_2 ... d_k in decimal then there are integers m_1 m_2 ... m_k > 0 such that n = d_1^m_1 + ... + d_k^m_k.

EXAMPLE

43 = 4^2 + 3^3 is OK; 254 = 2^7 + 5^3 + 4^0 is not OK since one of the powers is 0.

MAPLE

N:= 10000; # to get all entries <= N

Sums:= proc(L, N)

  option remember;

  local x1, L1;

  x1:= L[1];

  if x1 = 1 then L1:= {1}

  else L1:= {seq(x1^j, j=1..floor(log[x1](N)))};

  fi;

  if nops(L) = 1 then L1

  else select(`<=`, {seq(seq(a+b, a=L1), b=Sums(L[2..-1], N))}, N)

  fi

end proc;

filter:= proc(x, N)

   local L;

   L:= sort(subs(0=NULL, convert(x, base, 10))) ;

   member(x, Sums(L, N));

end proc;

A007532:= select(filter, [$1..N], N); # Robert Israel, Apr 13 2014

PROG

(Haskell)

a007532 n = a007532_list !! (n-1)

a007532_list = filter f [1..] where

   f x = g x 0 where

     g 0 v = v == x

     g u v = if d <= 1 then g u' (v + d) else v <= x && h d

             where h p = p <= x && (g u' (v + p) || h (p * d))

                   (u', d) = divMod u 10

-- Reinhard Zumkeller, Jun 02 2013

CROSSREFS

Cf. A001694, A005934, A005188, A003321, A014576, A023052, A046074.

Different from A061862.

Sequence in context: A228187 A134703 A061862 * A068189 A069716 A095289

Adjacent sequences:  A007529 A007530 A007531 * A007533 A007534 A007535

KEYWORD

base,nonn,nice

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified June 25 02:50 EDT 2017. Contains 288708 sequences.