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).
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
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Jan 25 2017
STATUS
approved