A281622 Numbers k such that sigma(k-1) is a Mersenne prime (A000668).

3, 5, 17, 26, 65, 4097, 65537, 262145, 1073741825

Offset: 1

Author

Jaroslav Krizek, Jan 25 2017

Keywords

• nonn
• more

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).

Examples

			65 is a term because sigma(64) = 127 (Mersenne prime).
		

Crossrefs

Union of 26 and odd terms of A270413.

Prime terms are in A249759.

Subsequence of A270413.

Cf. A000203, A000668, A256438.

Programs

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

Formula

Conjecture: a(n) = 2^A090748(n) + 1. - Daniel Suteu, Feb 08 2017