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%I #60 Mar 21 2020 16:39:03
%S 0,1,8,81,125,512,1000,1331,2592,6400,8000,10125,19683,20736,34300,
%T 35937,36125,46656,59319,74088,81000,123823,125000,157464,185193,
%U 268912,279936,328509,373248,421875,431244,469567,474552,481474,512000,592704,658503,795906
%N Numbers k such that k*sum_of_digits(k) is a perfect cube.
%H Derek Orr, <a href="/A227227/b227227.txt">Table of n, a(n) for n = 1..461</a>
%e 512*(5+1+2) = 4096 = 16^3. Hence, 512 is a term of the sequence.
%t Select[Range@ 1000000, IntegerQ@ Power[# Plus @@ IntegerDigits@ #, 1/3] == True &] (* _Michael De Vlieger_, Mar 23 2015 *)
%o (Python)
%o def DS(n):
%o return sum(int(i) for i in str(n))
%o def a(n):
%o k = 0
%o nDSn = n * DS(n)
%o while k <= n:
%o if k**3 == nDSn:
%o return True
%o if k**3 > nDSn:
%o return False
%o k += 1
%o [n for n in range(10**5) if a(n)]
%o # Simplified by _Derek Orr_, Mar 22 2015
%o (Sage)
%o n=100000 # change n for more terms
%o [x for x in [0..n] if floor((x*sum(Integer(x).digits(base=10)))^(1/3))==(x*sum(Integer(x).digits(base=10)))^(1/3)] # _Tom Edgar_, Sep 21 2013
%o (PARI) for(n=0, 10^6, if((n==0) || ispower(n*sumdigits(n), 3), print1(n, ", "))) \\ _Derek Orr_, Mar 22 2015
%Y Cf. A227224.
%K nonn,base,easy
%O 1,3
%A _Derek Orr_, Sep 19 2013
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