A272060 Numbers k such that sigma((k-1)/2) + tau((k-1)/2) is prime.

3, 5, 17, 257, 325, 1025, 65537, 82945, 202501, 250001, 2829125, 7496645, 10240001, 13675205, 16000001, 27060805, 48469445, 71402501, 133448705, 150062501, 156250001, 172186885, 182250001, 343064485, 354117125, 453519617, 467943425, 1235663105

Offset: 1

Author

Jaroslav Krizek, Apr 19 2016

Keywords

• nonn

Comments

Numbers k such that A000203((k-1)/2) + A000005((k-1)/2) is a prime q.

Corresponding values of primes q are in A055813.

Prime terms are in A272061.

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

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..5000

Crossrefs

Cf. A000005, A000203, A007503, A019434, A055813, A064205, A272061.

Programs

Magma

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

Mathematica

Select[Range[3, 10^7, 2], PrimeQ[DivisorSigma[1, #] + DivisorSigma[0, #]] &[(# - 1)/2] &] (* Michael De Vlieger, Apr 20 2016 *)

PARI

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

PARI

is(n)=my(f=factor(n\2)); n>2 && isprime(sigma(f)+numdiv(f)) && isprime(n) \\ Charles R Greathouse IV, Apr 29 2016

Formula

a(n) = 2*A064205(n) + 1.