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A254734
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a(n) is the least k > n such that n divides k^4.
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4
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2, 4, 6, 6, 10, 12, 14, 10, 12, 20, 22, 18, 26, 28, 30, 18, 34, 24, 38, 30, 42, 44, 46, 30, 30, 52, 30, 42, 58, 60, 62, 36, 66, 68, 70, 42, 74, 76, 78, 50, 82, 84, 86, 66, 60, 92, 94, 54, 56, 60, 102, 78, 106, 60, 110, 70, 114, 116, 118, 90, 122, 124, 84
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OFFSET
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1,1
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COMMENTS
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A073353(n) <= a(n) <= 2*n. Any prime that divides n must also divide a(n), and because n divides (2*n)^4.
a(n) = 2*n iff n is squarefree (A005117). - Robert Israel, Feb 08 2015
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LINKS
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Peter Kagey, Table of n, a(n) for n = 1..5000
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EXAMPLE
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a(16) = 18 because 16 divides 18^4, but 16 does not divide 17^4.
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MAPLE
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f:= proc(n) local k;
for k from n+1 do if (k^4/n)::integer then return k fi od:
end proc:
seq(f(n), n=1..100); # Robert Israel, Feb 08 2015
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MATHEMATICA
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lk[n_]:=Module[{k=n+1}, While[PowerMod[k, 4, n]!=0, k++]; k]; Array[lk, 70] (* Harvey P. Dale, Nov 22 2015 *)
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PROG
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(Ruby)
def a(n)
(n+1..2*n).find { |k| k**4 % n == 0 }
end
(PARI) a(n)=for(k=n+1, 2*n, if(k^4%n==0, return(k)))
vector(100, n, a(n)) \\ Derek Orr Feb 07 2015
(Python)
def A254734(n):
....k = n + 1
....while pow(k, 4, n):
........k += 1
....return k # Chai Wah Wu, Feb 15 2015
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CROSSREFS
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Cf. A005117 (squarefree).
Cf. A073353 (similar, with k^n).
Cf. A254732 (similar, with k^2), A254733 (similar, with k^3).
Sequence in context: A037225 A060685 A073353 * A254733 A254732 A299541
Adjacent sequences: A254731 A254732 A254733 * A254735 A254736 A254737
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KEYWORD
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nonn
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AUTHOR
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Peter Kagey, Feb 07 2015
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STATUS
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approved
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