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A279069
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Smallest k such that 1 + p + p^2 + p^3 + ... + p^k is prime, where p is the n-th prime.
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1
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1, 2, 2, 4, 16, 4, 2, 18, 4, 4, 6, 12, 2, 4, 126, 10, 2, 6, 18, 2, 4, 4, 4, 2, 16, 2, 18, 16, 16, 22, 4, 2, 10, 162, 6, 12, 16, 6, 2, 2, 18, 16, 16, 4, 30, 576, 40, 238, 4, 10, 112, 4, 16, 6, 22, 4
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OFFSET
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1,2
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COMMENTS
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Equivalently, smallest k such that (p^(k+1)-1)/(p-1) is prime, where p is the n-th prime.
For p prime, the sum of divisors of p^k is Sum_{j=0..k} p^j, so a(n) is the smallest k such that sigma(prime(n)^k) is prime, where sigma is the sum of divisors function A000203.
For the corresponding primes Sum_{j=0..k} p^j, see A279068.
a(57) > 10000. Next several terms after a(57) are 40, 4, a(60), 28, 2, 52, a(64), 108, 156, a(67), 4, 336; unknown terms a(60), a(64), and a(67) each exceed 5000.
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LINKS
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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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STATUS
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approved
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