A227225 Numbers k such that (sum of digits of k) + (product of digits of k) is a perfect cube.

0, 4, 10, 22, 36, 63, 80, 100, 107, 113, 128, 131, 170, 177, 182, 206, 218, 260, 269, 281, 296, 305, 311, 350, 404, 440, 503, 530, 602, 620, 629, 692, 701, 710, 717, 771, 800, 812, 821, 926, 962, 1000, 1007, 1016, 1025, 1034, 1043, 1052, 1061, 1070, 1106, 1160, 1168, 1186, 1205, 1233, 1250, 1304, 1323, 1332, 1340, 1349, 1394, 1403, 1430

Offset

1,2

Links

Table of n, a(n) for n=1..65.

Example

For 311, (3+1+1) + (3*1*1) = 5 + 3 = 8 = 2^3. Hence, 311 is a member of the sequence.

Mathematica

sdpdQ[n_]:=Module[{idn=IntegerDigits[n]}, IntegerQ[Surd[Total[ idn]+ Times@@idn, 3]]]; Select[Range[0, 1500], sdpdQ] (* Harvey P. Dale, Apr 05 2016 *)

Prog

(Python)
def DS(n):
  s = 0
  for i in str(n):
    s += int(i)
  return s
def DP(n):
  p = 1
  for i in str(n):
    p *= int(i)
  return p
for n in range(2000):
  k = 0
  while k**3 <= DS(n)+DP(n):
    if k**3 == DS(n)+DP(n):
      print(n, end=', ')
      break
    else:
      k += 1
## Edited by Derek Orr, Apr 10 2015
(PARI) for(n=0, 2000, d=digits(n); p=prod(i=1, #d, d[i]); s=sumdigits(n); if(ispower(s+p, 3), print1(n, ", "))) \\ Derek Orr, Apr 10 2015

Crossrefs

Cf. A161349

Sequence in context: A112774 A352296 A369385 * A008178 A009891 A301077

Adjacent sequences: A227222 A227223 A227224 * A227226 A227227 A227228

Keyword

nonn,base,easy

Author

Derek Orr, Sep 19 2013

Extensions

More terms from Derek Orr, Apr 10 2015

Status

approved