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

1,1

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)

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A064205, A065061.

Sequence in context: A305524 A326099 A171461 * A240410 A061250 A183813

Adjacent sequences: A065113 A065114 A065115 * A065117 A065118 A065119

Keyword

nonn

Author

Robert G. Wilson v, Nov 12 2001

Extensions

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

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

Status

approved