A246914 Primes p such that sigma(2p+1) = 3*(p+1).

7, 103, 1487, 9679, 73727, 603679

Offset: 1

Author

Jaroslav Krizek, Sep 07 2014

Keywords

• nonn
• more

Comments

Primes p such that sigma(p+sigma(p)) = 3*sigma(p). Subsequence of A246910.

The next term, if it exists, must be greater than 10^9.

Conjecture: Also primes p such that sigma(2p+1) mod p = 3. - Jaroslav Krizek, Sep 28 2014

No other terms up to 10^11. - Michel Marcus, Feb 21 2020

Examples

			Prime 7 is in sequence because sigma(2*7 + 1) = sigma(15) = 24 = 3*(7+1).
		

Crossrefs

Cf. A000203, A246456, A246910.

Programs

Magma

[n:n in[1..10^7] | SumOfDivisors(n+SumOfDivisors(n))eq 3*SumOfDivisors(n) and IsPrime(n)]

Maple

with(numtheory): A246914:=n->`if`(isprime(n) and sigma(2*n+1) = 3*(n+1), n, NULL): seq(A246914(n), n=1..10^5); # Wesley Ivan Hurt, Oct 01 2014

Mathematica

Select[Prime[Range[1500]], DivisorSigma[1, 2# + 1] == 3# + 3 &] (* Alonso del Arte, Sep 07 2014 *)

PARI

for(n=1,10^6,p=prime(n);if(sigma(p+sigma(p))==3*sigma(p),print1(p,", "))) \\ Derek Orr, Sep 07 2014

PARI

forprime(p=2,10^7,if(sigma(2*p+1)==3*(p+1),print1(p,","))) \\ Edward Jiang, Sep 07 2014