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A281622
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Numbers n such that sigma(n-1) is a Mersenne prime (A000668).
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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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Conjecture 1: the next terms are: 1152921504606846977, 309485009821345068724781057, 81129638414606681695789005144065, 85070591730234615865843651857942052865.
Conjecture 2: Union of 26 and A256438.
Conjecture 3: Mersenne prime 31 is the only prime p such that p = sigma(x-1) = sigma(y-1) for distinct numbers x and y; 31 = sigma(17-1) = sigma(26-1).
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LINKS
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FORMULA
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EXAMPLE
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65 is a term because sigma(64) = 127 (Mersenne prime).
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PROG
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(Magma) [n: n in[2..1000000], k in [1..20] | SumOfDivisors(n-1) eq 2^k-1 and IsPrime(2^k-1)]
(PARI) isok(n) = my(s = sigma(n-1)); isprime(s) && ispower(s+1, , &p) && (p==2); \\ Michel Marcus, Jan 27 2017
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CROSSREFS
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Union of 26 and odd terms of A270413.
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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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