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A061862 Powerful numbers (2a): a sum of nonnegative powers of its digits.

%I A061862 #14 Nov 21 2019 22:12:48
%S A061862 0,1,2,3,4,5,6,7,8,9,24,43,63,89,132,135,153,175,209,224,226,254,258,
%T A061862 262,263,264,267,283,332,333,334,347,357,370,371,372,373,374,375,376,
%U A061862 377,378,379,407,445,463,472,518,538,598,629,635,653,675,730,731,732
%N A061862 Powerful numbers (2a): a sum of nonnegative powers of its digits.
%C A061862 Zero digits cannot be used in the sum. - _N. J. A. Sloane_, Aug 31 2009
%C A061862 More precisely, digits 0 do not contribute to the sum, in contrast to A134703 where it is allowed to use 0^0 = 1. - _M. F. Hasler_, Nov 21 2019
%H A061862 D. Wilson, <a href="/A061862/b061862.txt">Table of n, a(n) for n=1..10000</a>
%H A061862 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>
%F A061862 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.
%e A061862 43 = 4^2 + 3^3; 254 = 2^7 + 5^3 + 4^0 = 128 + 125 + 1.
%e A061862 209 = 2^7 + 9^2.
%e A061862 732 = 7^0 + 3^6 + 2^1.
%t A061862 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 ] ] ]
%o A061862 (Haskell)
%o A061862 a061862 n = a061862_list !! (n-1)
%o A061862 a061862_list = filter f [0..] where
%o A061862    f x = g x 0 where
%o A061862      g 0 v = v == x
%o A061862      g u v = if d <= 1 then g u' (v + d) else v <= x && h 1
%o A061862              where h p = p <= x && (g u' (v + p) || h (p * d))
%o A061862                    (u', d) = divMod u 10
%o A061862 -- _Reinhard Zumkeller_, Jun 02 2013
%Y A061862 Cf. A001694, A005934, A005188, A003321, A014576, A023052, A046074.
%Y A061862 Different from A007532 and A134703, which are variations.
%K A061862 base,nonn
%O A061862 1,3
%A A061862 _Erich Friedman_, Jun 23 2001