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A229185 Numbers incremented by their digit product produce a cube.

%I A229185 #29 Oct 16 2024 14:52:42
%S A229185 0,4,85,168,184,212,368,549,681,919,999,1000,1283,1593,2181,3664,4096,
%T A229185 4717,6811,7497,8000,9919,10648,12143,15275,15425,21664,21728,21824,
%U A229185 27000,39304,42427,42811,47629,50653,63424,64000,74088,79507,84416,103823,110592
%N A229185 Numbers incremented by their digit product produce a cube.
%e A229185 681 + 6*8*1 = 729 = 9^3.
%t A229185 Select[Range[0,100000], IntegerQ[(# + Times @@ IntegerDigits[#])^(1/3)] &] (* _T. D. Noe_, Sep 16 2013 *)
%o A229185 (Python)
%o A229185 def DP(n):
%o A229185   p = 1
%o A229185   for i in str(n):
%o A229185     p *= int(i)
%o A229185   return p
%o A229185 for n in range(10**4):
%o A229185   k = 0
%o A229185   P = n + DP(n)
%o A229185   while P >= k**3:
%o A229185     if P == k**3:
%o A229185       print(n, end=', ')
%o A229185       break
%o A229185     k += 1
%o A229185 # Simplified by _Derek Orr_, Mar 12 2015
%o A229185 (PARI) for(n=0, 10^5, d=digits(n); P=n+prod(i=1, #d, d[i]); if(ispower(P, 3), print1(n, ", "))) \\ _Derek Orr_, Mar 12 2015
%Y A229185 Cf. A007954, A066567, A229184.
%K A229185 nonn,easy,base
%O A229185 1,2
%A A229185 _Derek Orr_, Sep 15 2013
%E A229185 Prepended a(1) = 0 from _Derek Orr_, Mar 12 2015