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

1,1

Comments

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

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

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

Supersequence of A249759.

Links

Table of n, a(n) for n=1..12.

Formula

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

Example

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

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 *)

Prog

(Magma) [n: n in[2..10000000] | SumOfDivisors(SumOfDivisors(n-1)) eq 2*(n-1)]
(PARI) isok(m) = sigma(sigma(m-1)) == 2*(m-1); \\ Michel Marcus, Feb 09 2020

Crossrefs

Cf. A000203, A051027, A019279, A249759.

Sequence in context: A350142 A278741 A265425 * A251737 A125957 A259908

Adjacent sequences: A256435 A256436 A256437 * A256439 A256440 A256441

Keyword

nonn,more

Author

Jaroslav Krizek, Mar 29 2015

Status

approved