A256438 Numbers m such that sigma(sigma(m-1)) = 2*(m-1).

3, 5, 17, 65, 4097, 65537, 262145, 1073741825, 1152921504606846977, 309485009821345068724781057, 81129638414606681695789005144065, 85070591730234615865843651857942052865

Offset: 1

Author

Jaroslav Krizek, Mar 29 2015

Keywords

• nonn
• more

Comments

Numbers k such that A051027(k-1) = 2*(k-1).

Conjecture: numbers of the form 2^k+1 such that sigma(2^k) = prime p.

Prime terms: 3, 5, 17, 65537, ...

Supersequence of A249759.

Examples

			17 is in the sequence because sigma(sigma(17-1)) = 32 = 2*(17-1).
		

Crossrefs

Cf. A000203, A051027, A019279, A249759.

Programs

Magma

[n: n in[2..10000000] | SumOfDivisors(SumOfDivisors(n-1)) eq 2*(n-1)];

Maple

with(numtheory): A256438:=n->`if`(sigma(sigma(n-1)) = 2*(n-1), n, NULL): seq(A256438(n), n=2..10^5); # Wesley Ivan Hurt, Mar 30 2015

Mathematica

Select[Range@ 1000000, DivisorSigma[1, DivisorSigma[1, # - 1]] == 2 (# - 1) &] (* Michael De Vlieger, Mar 29 2015 *)

PARI

isok(m) = sigma(sigma(m-1)) == 2*(m-1); \\ Michel Marcus, Feb 09 2020

Formula

a(n) = A019279(n) + 1. - Michel Marcus, Feb 09 2020