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A257567
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a(n) is the largest exponent k such that 3^k divides (prime(n)^2 + 2).
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2
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1, 0, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 1, 2, 1, 2, 2, 1, 3, 1, 3, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 1, 4, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2
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OFFSET
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1,3
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COMMENTS
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Except for n=2, all a(n) > 1 because (prime(n)^2 + 2) is divisible by 3.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 1 because p=prime(1)=2 and p^2 + 2 = 6 = 3^1*2,
a(2) = 0 because p=prime(2)=3 and p^2 + 2 = 11 = 3^0*11,
a(3) = 3 because p=prime(3)=5 and p^2 + 2 = 27 = 3^3.
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MATHEMATICA
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Table[IntegerExponent[Prime[k]^2 + 2, 3], {k, 100}]
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PROG
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(PARI) a(n) = valuation(prime(n)^2+2, 3); \\ Michel Marcus, May 01 2015
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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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