A341286 Numbers k such that k plus the sum of the fifth powers of the digits of k is a cube.

0, 2435, 3403, 5625, 8781, 11140, 22664, 23325, 32908, 33346, 34822, 41332, 58555, 99180, 103925, 109272, 133118, 136386, 145263, 170740, 180105, 182142, 194261, 207459, 208813, 228224, 249945, 251991, 266080, 305840, 341539, 351824, 359720, 372287, 380064, 415434

Offset: 1

Author

Will Gosnell, Feb 08 2021

Keywords

• base
• nonn
• less

Examples

			2435 is a term since 2435 + 2^5 + 4^5 + 3^5 + 5^5 = 19^3;
3403 is a term since 3403 + 3^5 + 4^5 + 0^5 + 3^5 = 17^3.
		

Crossrefs

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

Programs

Maple

filter:= proc(n) local x, d;
  x:= n + add(d^5, d = convert(n, base, 10));
  surd(x, 3)::integer
end proc:
select(filter, [$0..10^5]); # Robert Israel, Feb 09 2021

Mathematica

Select[Range[0, 500000], IntegerQ@ Power[# + Total[IntegerDigits[#]^5], 1/3] &] (* Michael De Vlieger, Feb 22 2021 *)
Select[Range[0,416000],IntegerQ[Surd[#+Total[IntegerDigits[#]^5],3]]&] (* Harvey P. Dale, Jul 19 2022 *)

PARI

isok(k) = ispower(k+vecsum(apply(x->x^5, digits(k))), 3); \\ Michel Marcus, Feb 09 2021

Python

from sympy import integer_nthroot
def powsum(n): return sum(int(d)**5 for d in str(n))
def ok(n): return integer_nthroot(n + powsum(n), 3)[1]
def aupto(lim):
  alst = []
  for k in range(lim+1):
    if ok(k): alst.append(k)
  return alst
print(aupto(415434)) # Michael S. Branicky, Feb 22 2021

Extensions

More terms from Michel Marcus, Feb 09 2021

a(1)=0 prepended by Michael S. Branicky, Feb 22 2021