A065116 Numbers k such that sigma(k) + tau(k) and sigma(k) - tau(k) are primes.

8, 162, 512, 32768, 41472, 3748322, 5120000, 6837602, 8000000, 35701250, 75031250, 78125000, 91125000, 907039232, 10660336128, 11911961250, 21234895362, 41265473762, 55965865922, 209642370242, 835707290112, 1148179179938, 1821331173888, 2097152000000

Offset: 1

Author

Robert G. Wilson v, Nov 12 2001

Keywords

• nonn

Comments

Intersection of A064205 and A065061.

From Kevin P. Thompson, Jun 20 2022: (Start)

Terms must be twice a square (see A064205).

No terms are congruent to 4 or 6 (mod 10) (see A064205). (End)

Examples

			162 is a term since sigma(162) = 363 and tau(162) = 10 are numbers whose sum (373) and difference (353) are both primes.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A064205, A065061.

Programs

Mathematica

Do[ds1 = DivisorSigma[1, n]; ds0 = DivisorSigma[0, n]; If[ PrimeQ[ds1 + ds0] && PrimeQ[ds1 - ds0], Print[n]], {n, 1, 10^7} ]

Extensions

a(10)-a(19) from Donovan Johnson, Jul 09 2010

a(20)-a(24) from Donovan Johnson, Aug 23 2013