%I #37 Jul 19 2022 16:20:50

%S 0,2435,3403,5625,8781,11140,22664,23325,32908,33346,34822,41332,

%T 58555,99180,103925,109272,133118,136386,145263,170740,180105,182142,

%U 194261,207459,208813,228224,249945,251991,266080,305840,341539,351824,359720,372287,380064,415434

%N Numbers k such that k plus the sum of the fifth powers of the digits of k is a cube.

%e 2435 is a term since 2435 + 2^5 + 4^5 + 3^5 + 5^5 = 19^3;

%e 3403 is a term since 3403 + 3^5 + 4^5 + 0^5 + 3^5 = 17^3.

%p filter:= proc(n) local x, d;

%p x:= n + add(d^5, d = convert(n, base, 10));

%p surd(x, 3)::integer

%p end proc:

%p select(filter, [$0..10^5]); # _Robert Israel_, Feb 09 2021

%t Select[Range[0, 500000], IntegerQ@ Power[# + Total[IntegerDigits[#]^5], 1/3] &] (* _Michael De Vlieger_, Feb 22 2021 *)

%t Select[Range[0,416000],IntegerQ[Surd[#+Total[IntegerDigits[#]^5],3]]&] (* _Harvey P. Dale_, Jul 19 2022 *)

%o (PARI) isok(k) = ispower(k+vecsum(apply(x->x^5, digits(k))), 3); \\ _Michel Marcus_, Feb 09 2021

%o (Python)

%o from sympy import integer_nthroot

%o def powsum(n): return sum(int(d)**5 for d in str(n))

%o def ok(n): return integer_nthroot(n + powsum(n), 3)[1]

%o def aupto(lim):

%o alst = []

%o for k in range(lim+1):

%o if ok(k): alst.append(k)

%o return alst

%o print(aupto(415434)) # _Michael S. Branicky_, Feb 22 2021

%Y Cf. A055014 (sum of 5th powers of digits).

%K base,nonn,less

%O 1,2

%A _Will Gosnell_, Feb 08 2021

%E More terms from _Michel Marcus_, Feb 09 2021

%E a(1)=0 prepended by _Michael S. Branicky_, Feb 22 2021