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A252041
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Numbers n such that n - 3 divides n^n + 3.
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4
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1, 2, 4, 5, 6, 9, 10, 85, 105, 136, 186, 262, 820, 1161, 2626, 2926, 4924, 10396, 11656, 19689, 27637, 33736, 36046, 42886, 42901, 53866, 55189, 82741, 95266, 103762, 106822, 127401, 135460, 251506, 366796, 375220, 413326, 466966, 531445, 553456, 568876
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OFFSET
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1,2
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COMMENTS
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Numbers n such that (n^n + 3)/(n - 3) is an integer.
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LINKS
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EXAMPLE
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2 is in this sequence because (2^2 + 3)/(2 - 3) = -7 is an integer.
4 is in this sequence because (4^4 + 3)/(4 - 3) = 259 is an integer.
7 is not in the sequence because (7^7 + 3)/4 = 411773/2, which is not an integer.
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MAPLE
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select(t -> 3 &^t + 3 mod (t-3) = 0, [1, 2, $4..10^6]); # Robert Israel, Dec 19 2014
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MATHEMATICA
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PROG
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(Magma) [n: n in [4..50000] | Denominator((n^n+3)/(n-3)) eq 1];
(PARI) isok(n) = (n != 3) && (Mod(n, n-3)^n == -3); \\ Michel Marcus, Dec 13 2014
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CROSSREFS
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Cf. ...............Numbers n such that x divides y, where:
...x......y....k = 0.....k = 1.....k = 2......k = 3.......
(For x=n-1 and y=n^n+1, the only terms are 0, 2 and 3. - David L. Harden, Dec 28 2014}
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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