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A254732
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a(n) is the least k > n such that n divides k^2.
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4
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2, 4, 6, 6, 10, 12, 14, 12, 12, 20, 22, 18, 26, 28, 30, 20, 34, 24, 38, 30, 42, 44, 46, 36, 30, 52, 36, 42, 58, 60, 62, 40, 66, 68, 70, 42, 74, 76, 78, 60, 82, 84, 86, 66, 60, 92, 94, 60, 56, 60, 102, 78, 106, 72, 110, 84, 114, 116, 118, 90, 122, 124, 84, 72
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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)^2.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 + zeta(3)/zeta(2) = 1 + A253905 = 1.73076296940143849872... . - Amiram Eldar, Feb 17 2024
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EXAMPLE
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a(12) = 18 because 12 divides 18^2, but 12 does not divide 13^2, 14^2, 15^2, 16^2, or 17^2.
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MATHEMATICA
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lk[n_]:=Module[{k=n+1}, While[!Divisible[k^2, n], k++]; k]; Array[lk, 70] (* Harvey P. Dale, Nov 05 2017 *)
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PROG
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(Ruby)
def a(n)
(n+1..2*n).find { |k| k**2 % n == 0 }
end
(PARI)
a(n)=for(k=n+1, 2*n, if(k^2%n==0, return(k)))
vector(100, n, a(n)) \\ Derek Orr, Feb 06 2015
(PARI) a(n)=my(t=factorback(factor(n)[, 1])); forstep(k=n+t, 2*n, t, if(k^2%n==0, return(k))) \\ Charles R Greathouse IV, Feb 07 2015
(Haskell)
a254732 n = head [k | k <- [n + 1 ..], mod (k ^ 2) n == 0]
(Python)
....k = n + 1
....while pow(k, 2, n):
........k += 1
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CROSSREFS
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Cf. A254733 (similar, with k^3), A254734 (similar, with k^4), A073353 (similar, with limit m->infinity of k^m).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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