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

Author

Derek Orr, Sep 15 2013

Keywords

• nonn
• easy
• base

Examples

			681 + 6*8*1 = 729 = 9^3.
		

Crossrefs

Cf. A007954, A066567, A229184.

Programs

Mathematica

Select[Range[0,100000], IntegerQ[(# + Times @@ IntegerDigits[#])^(1/3)] &] (* T. D. Noe, Sep 16 2013 *)

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

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