A368651 Numbers k such that 2^sigma(k) - k is a prime.

3, 5, 17, 49, 53, 185, 503, 1301, 1689, 1797, 5929, 14747, 20433, 29903, 42137, 64763

Offset: 1

Author

J.W.L. (Jan) Eerland, Jan 02 2024

Keywords

• nonn
• more

Comments

If it exists, a(17) > 120000. - Michael S. Branicky, Aug 19 2024

Examples

			5 is in the sequence because 2^sigma(5)-5 = 2^6-5 = 59 is prime.
		

Crossrefs

Cf. A000043, A000203, A000668, A023194, A023195, A253850, A253851.

Programs

Magma

[n: n in[1..10000] | IsPrime((2^SumOfDivisors(n)) - n)];

Mathematica

a[n_] := Select[Range@ n, PrimeQ[2^DivisorSigma[1, #] - #] &]; a[20000]
DeleteCases[ParallelTable[If[PrimeQ[2^DivisorSigma[1,k]-k],k,n],{k,1,10^4}],n]

Extensions

a(16) from J.W.L. (Jan) Eerland, Jan 25 2024