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A215111
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Numbers n such that n^2+1 divides n!!.
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1
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70, 132, 182, 212, 216, 242, 268, 278, 294, 302, 342, 360, 378, 394, 408, 438, 500, 512, 524, 538, 560, 568, 580, 606, 616, 660, 682, 684, 746, 748, 772, 776, 788, 798, 818, 822, 850, 882, 914, 922, 924, 948, 970, 1032, 1034, 1048, 1068, 1084, 1118, 1148, 1168
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OFFSET
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1,1
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COMMENTS
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a(n) is even.
Even numbers n such that n^2+1 divides (n/2)!. - Robert Israel, Jun 19 2019
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LINKS
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FORMULA
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EXAMPLE
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70 is in the sequence because 70^2+1 = 4901 = 29*13^2 divides 70!!= 355044260642859198243475901411974413130137600000000 =
2 ^ 67 *3 ^ 15
*5 ^ 8 * 7 ^ 5 * 11 ^ 3 * 13 ^ 2 * 17 ^ 2 *19 * 23 * 29* 31
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MAPLE
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with(numtheory):for n from 1 to 1300 do:x:=irem(doublefactorial(n), n^2+1): if x=0 then printf(`%d, `, n):else fi:od:
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MATHEMATICA
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Select[Range[1200], Divisible[#!!, #^2+1]&] (* Harvey P. Dale, Oct 14 2015 *)
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CROSSREFS
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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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