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A341286 Numbers k such that k plus the sum of the fifth powers of the digits of k is a cube. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

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.

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A147984 A229871 A192767 * A250710 A278196 A032734

Adjacent sequences:  A341283 A341284 A341285 * A341287 A341288 A341289

KEYWORD

base,nonn,less

AUTHOR

Will Gosnell, Feb 08 2021

EXTENSIONS

More terms from Michel Marcus, Feb 09 2021

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

STATUS

approved

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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)