OFFSET
1,1
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..235
EXAMPLE
sigma((17-1)/2) + tau((17-1)/2) = sigma(8) + tau(8) = 15 + 4 = 19; 19 is prime, so 17 is in the sequence.
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 *)
PROG
(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]
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Apr 19 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
STATUS
approved