A255510 Numbers n of the form 3^k such that sigma(n) is a prime p.

9, 729, 531441, 2503155504993241601315571986085849, 4638397686588101979328150167890591454318967698009

Offset: 1

Author

Jaroslav Krizek, Mar 25 2015

Keywords

• nonn

Comments

Powers of 3 from A023194 (numbers n such that sigma(n) is a prime).

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..10

Crossrefs

Cf. A000203 (sigma), A023194 (sigma(n) is prime).

Cf. A003462 (sigma(3^n)), A028491 (sigma(3^n) is prime) , A076481.

Programs

Magma

[(3^n): n in [1..1000] | IsPrime((SumOfDivisors(3^n)))]

Mathematica

Select[3^Range[0,110],PrimeQ[DivisorSigma[1,#]]&] (* Harvey P. Dale, Mar 29 2015 *)

Formula

a(n) = 3^(A028491(n) - 1).

sigma(a(n)) = A076481(n).