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A116891
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a(n) = gcd(n! + 1, n^n + 1).
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4
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2, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 47, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 79, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 103, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 127, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 191, 1, 1, 1, 199, 1, 1
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OFFSET
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1,1
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COMMENTS
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Apparently all the values greater than 1 (cf. A116892) are prime numbers and are equal to 2n+1 with only 4 exceptions for n<82000 (cf. A116894).
The first duplicated value > 1 is 157519 = a(43755) = a(78759). Note that 43755 = 15*2917, while 78759 = 27*2917.
It seems that for the long time after a(1) = 2, all other terms > 1 occur only at such positions k that k+1 is not squarefree. However, this turns out to be false as a(208161) = 555097, and 208162 is a squarefree number.
(End)
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LINKS
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EXAMPLE
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a(3) = gcd(3! + 1, 3^3 + 1) = gcd(7,28) = 7.
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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