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A061862 Powerful numbers (2a): a sum of nonnegative powers of its digits. 4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 43, 63, 89, 132, 135, 153, 175, 209, 224, 226, 254, 258, 262, 263, 264, 267, 283, 332, 333, 334, 347, 357, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 407, 445, 463, 472, 518, 538, 598, 629, 635, 653, 675, 730, 731, 732 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Zero digits cannot be used in the sum. - N. J. A. Sloane, Aug 31 2009

LINKS

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

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; 254 = 2^7 + 5^3 + 4^0 = 128 + 125 + 1.

209 = 2^7 + 9^2.

732 = 7^0 + 3^6 + 2^1.

MATHEMATICA

f[ n_ ] := Module[ {}, a=IntegerDigits[ n ]; e=g[ Length[ a ] ]; MemberQ[ Map[ Apply[ Plus, a^# ] &, e ], n ] ] g[ n_ ] := Map[ Take[ Table[ 0, {n} ]~Join~#, -n ] &, IntegerDigits[ Range[ 10^n ], 10 ] ] For[ n=0, n >= 0, n++, If[ f[ n ], Print[ n ] ] ]

PROG

(Haskell)

a061862 n = a061862_list !! (n-1)

a061862_list = filter f [0..] 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 1

             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 A007532 and A134703, which are variations.

Sequence in context: A126957 A228187 A134703 * A007532 A068189 A069716

Adjacent sequences:  A061859 A061860 A061861 * A061863 A061864 A061865

KEYWORD

base,nonn

AUTHOR

Erich Friedman, Jun 23 2001

STATUS

approved

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Last modified May 24 18:18 EDT 2017. Contains 286997 sequences.