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A281312
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Numbers n such that sigma(4*(n-1)) is prime.
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2
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2, 5, 17, 1025, 16385, 65537, 268435457, 288230376151711745, 77371252455336267181195265, 20282409603651670423947251286017, 21267647932558653966460912964485513217
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OFFSET
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1,1
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COMMENTS
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Conjecture: the next terms are: 288230376151711745, 77371252455336267181195265, 20282409603651670423947251286017, 21267647932558653966460912964485513217.
Conjecture: prime terms are in A258429: 2, 5, 17, 65537.
Conjecture: corresponding primes p are Mersenne primes (A000668) > 3.
Sigma is multiplicative, and sigma(m) > 1 for all m > 1, so sigma(m) can be prime only if m is a prime power. Hence all n in this sequence are of the form 2^m + 1 for some m >= 0. This proves the above conjectures and leads to an explicit formula (q.v.) in terms of the Mersenne numbers. - Charles R Greathouse IV, Mar 01 2017
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LINKS
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FORMULA
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PROG
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(Magma) [n: n in [2..100000] | IsPrime(SumOfDivisors(4*(n-1)))]
(PARI) isok(n) = isprime(sigma(4*(n-1))); \\ Michel Marcus, Jan 21 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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