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A341286
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Numbers k such that k plus the sum of the fifth powers of the digits of k is a cube.
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0
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MAPLE
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filter:= proc(n) local x, d;
x:= n + add(d^5, d = convert(n, base, 10));
surd(x, 3)::integer
end proc:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A055014 (sum of 5th powers of digits).
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KEYWORD
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base,nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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