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A283515
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Numbers k such that sigma(k^(k-1)) is a prime.
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0
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OFFSET
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1,1
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COMMENTS
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sigma(k) is the sum of the divisors of k (A000203).
a(8) > 10^4.
Corresponding values of k^(k-1): 2, 9, 64, 1152921504606846976, ...
Corresponding values of sigma(k^(k-1)): 3, 13, 127, 2305843009213693951, ...
Subsequence of A280257 (numbers k such that tau(k^(k-1)) is prime).
For k < 1000, sigma(k^(k+1)) is prime only for k = 5: sigma(5^6) = sigma(15625) = 19531 (prime).
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LINKS
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EXAMPLE
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sigma(4^3) = sigma(64) = 127 (prime).
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MATHEMATICA
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fQ[n_] := PrimeQ[DivisorSigma[1, n^(n - 1)]]; Select[Range@1000, fQ] (* Robert G. Wilson v, Mar 10 2017 *)
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PROG
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(Magma) [n: n in [1..500] | IsPrime(SumOfDivisors(n^(n-1)))]
(PARI) isok(n) = isprime(sigma(n^(n-1))); \\ Michel Marcus, Mar 10 2017
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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