A272061 Primes p such that sigma((p-1)/2) + tau((p-1)/2) is prime.

3, 5, 17, 257, 65537, 453519617, 1372257937, 1927561217, 21320672257, 76001667857, 138388464037, 1216026685697, 2085136000001, 8503056000001, 30118144000001, 35427446793217, 37015056000001, 83037656250001, 87329473560577, 97850397828097, 222330465562501, 233952748524197

Offset: 1

Author

Jaroslav Krizek, Apr 19 2016

Keywords

• nonn

Comments

Primes p such that A007503((p-1)/2) is a prime q.

Corresponding values of primes q: 2, 5, 19, 263, 65551, 496922891, ...

Prime terms from A272060.

The first 5 known Fermat primes from A019434 are in this sequence.

Primes of the form 2*m+1 with m a term of A064205. - Michel Marcus, Apr 25 2016

Examples

			sigma((17-1)/2) + tau((17-1)/2) = sigma(8) + tau(8) = 15 + 4 = 19; 19 is prime, so 17 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..235

Crossrefs

Cf. A000005, A000203, A007503, A055813, A064205, A272060.

Programs

Magma

[n: n in [3..1000000] | IsPrime(n) and IsPrime(NumberOfDivisors((n-1) div 2) + SumOfDivisors((n-1) div 2)) and (n-1) mod 2 eq 0];

Maple

with(numtheory): A272061:=n->`if`(isprime(n) and isprime(sigma((n-1)/2)+tau((n-1)/2)), n, NULL): seq(A272061(n), n=3..10^5); # Wesley Ivan Hurt, Apr 20 2016

Mathematica

Select[Prime[Range[10000]],PrimeQ[DivisorSigma[1,(#-1)/2] + DivisorSigma[0,(#-1)/2]] & ] (* Robert Price, Apr 21 2016 *)

PARI

isok(n) = isprime(sigma((n-1)/2) + numdiv((n-1)/2));
lista(nn) = forprime (p=3, nn, if (isok(p), print1(p, ", "))); \\ Michel Marcus, Apr 19 2016

PARI

is(n)=my(f=factor(n\2)); isprime(sigma(f)+numdiv(f)) && isprime(n) \\ Charles R Greathouse IV, Apr 28 2016

Extensions

a(7)-a(8) from Michel Marcus, Apr 24 2016

a(9) from Charles R Greathouse IV, Apr 29 2016

a(10) from Charles R Greathouse IV, Apr 29 2016

a(11)-a(20), using A064205 bfile, added by Michel Marcus, Nov 23 2022

a(21)-a(22) from Amiram Eldar, Dec 06 2022