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A281622 Numbers n such that sigma(n-1) is a Mersenne prime (A000668). 0
3, 5, 17, 26, 65, 4097, 65537, 262145, 1073741825 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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).
LINKS
FORMULA
Conjecture: a(n) = 2^A090748(n) + 1. - Daniel Suteu, Feb 08 2017
EXAMPLE
65 is a term because sigma(64) = 127 (Mersenne prime).
PROG
(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
CROSSREFS
Union of 26 and odd terms of A270413.
Prime terms are in A249759.
Subsequence of A270413.
Sequence in context: A025111 A253204 A266165 * A256439 A256444 A032619
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Jan 25 2017
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)