A247821 Numbers k such that sigma(sigma(2k-1)) is a prime p.

2, 1334, 1969, 28669, 86006, 126961, 338603654, 536801281, 366479720500691270, 375344017599431990, 500461553802019261, 554079264075351985

Offset: 1

Author

Jaroslav Krizek, Sep 28 2014

Keywords

• nonn
• more

Comments

Numbers n such that A000203(A000203(2n-1)) = A000203(A008438(n-1)) = A051027(2n-1) is a prime p.

Corresponding values of primes p are 7, 8191, 8191, 131071, 524287, 524287, ... (= A247822). Conjecture: The primes p are Mersenne primes (A000668).

sigma(sigma(2*a(9)-1)) > 10^16.

If the above conjecture is true, the next terms are 366479720500691270, 375344017599431990, 500461553802019261, 554079264075351985, 98375588019240949991670086, ... . - Hiroaki Yamanouchi, Oct 01 2014

a(13) > 5*10^18. - Giovanni Resta, Feb 14 2020

Examples

			Number 1334 is in sequence because sigma(sigma(2*1334-1)) = sigma(sigma(2667)) = sigma(4096) = 8191, i.e., prime.
		

Crossrefs

Cf. A000203, A008438, A247790, A247791, A247820, A247822, A247823, A247954.

Programs

Magma

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

Mathematica

Select[Range[10^6], PrimeQ[DivisorSigma[1, DivisorSigma[1, 2 # - 1]]] &] (* Robert Price, May 17 2019 *)

PARI

for(n=1,10^7,if(ispseudoprime(sigma(sigma(2*n-1))),print1(n,", "))) \\ Derek Orr, Sep 29 2014

Formula

a(n) = (A247838(n) +1) / 2.

a(n)-1 = numbers n such that sigma(sigma(2n+1)) is a prime p: 1, 1333, 1968, 28668, 86005, 126960, ...

Extensions

a(7)-a(8) from Hiroaki Yamanouchi, Oct 01 2014

a(9)-a(12) from Giovanni Resta, Feb 14 2020