A229184 Numbers decremented by their digit product produce a cube.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 71, 145, 167, 264, 361, 757, 1000, 1439, 1791, 2233, 3525, 3627, 3959, 4096, 4864, 4995, 6677, 8000, 8128, 8672, 9575, 10648, 14848, 23488, 24976, 25199, 25829, 26549, 27000, 27224, 35648, 39304, 43235, 50653, 53893, 64000, 74088, 79507, 91215, 93285, 94365
Offset: 1
Examples
167 - 1*6*7 = 125 = 5^3.
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
More terms and prepended a(1) = 0 from Derek Orr, Mar 12 2015
Comments