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A309355
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Even numbers k such that k! is divisible by k*(k+1)/2.
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0
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8, 14, 20, 24, 26, 32, 34, 38, 44, 48, 50, 54, 56, 62, 64, 68, 74, 76, 80, 84, 86, 90, 92, 94, 98, 104, 110, 114, 116, 118, 120, 122, 124, 128, 132, 134, 140, 142, 144, 146, 152, 154, 158, 160, 164, 168, 170, 174, 176, 182, 184, 186, 188, 194, 200, 202, 204, 206
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OFFSET
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1,1
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COMMENTS
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And A071904 are the successors of a(n).
Even numbers that are not a prime - 1. That is, even numbers not in A006093. - Terry D. Grant, Oct 31 2020
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REFERENCES
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J. D. E. Konhauser et al., Which Way Did The Bicycle Go?, Problem 98, pp. 29; 145-146, MAA Washington DC, 1996.
Die WURZEL - Zeitschrift für Mathematik, 53. Jahrgang, Juli 2019, S. 171, WURZEL-Aufgabe 2019-36 von Gerhard Dietel, Regensburg.
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LINKS
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FORMULA
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EXAMPLE
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8! = 40320 is divisible by 8*9/2 = 36.
14! is divisible by 14*15/2.
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MATHEMATICA
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Complement[Table[2 n, {n, 1, 103}], Table[EulerPhi[Prime[n]], {n, 1, 103}]] (* Terry D. Grant, Oct 31 2020 *)
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PROG
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(PARI) forcomposite(c=4, 10^3, if(c%2==1, print1(c-1, ", "))); \\ Joerg Arndt, Jul 25 2019
(Magma) [k: k in [2..250]|IsEven(k) and Factorial(k) mod Binomial(k+1, 2) eq 0]; // Marius A. Burtea, Jul 28 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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