A229185 Numbers incremented by their digit product produce a cube.
0, 4, 85, 168, 184, 212, 368, 549, 681, 919, 999, 1000, 1283, 1593, 2181, 3664, 4096, 4717, 6811, 7497, 8000, 9919, 10648, 12143, 15275, 15425, 21664, 21728, 21824, 27000, 39304, 42427, 42811, 47629, 50653, 63424, 64000, 74088, 79507, 84416, 103823, 110592
Offset: 1
Examples
681 + 6*8*1 = 729 = 9^3.
Programs
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Mathematica
Select[Range[0,100000], IntegerQ[(# + Times @@ IntegerDigits[#])^(1/3)] &] (* T. D. Noe, Sep 16 2013 *)
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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
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Python
def DP(n): p = 1 for i in str(n): p *= int(i) return p for n in range(10**4): k = 0 P = n + DP(n) while P >= k**3: if P == k**3: print(n, end=', ') break k += 1 # Simplified by Derek Orr, Mar 12 2015
Extensions
Prepended a(1) = 0 from Derek Orr, Mar 12 2015