A066110 Primes of the form sigma_4(k)/sigma_2(k), arising in A066109.

13, 73, 313, 601, 28393, 83233, 922561, 3416953, 13842121, 47451433, 141146281, 212601841, 234750601, 294482761, 2750006041, 3262751521, 4362404353, 4784281393, 5236041961, 9354855121, 9597826993, 13564461457, 16936647121

Offset: 1

Author

Labos Elemer, Dec 05 2001

Keywords

• nonn

Examples

			For k = 20: divisors(20) = {20,10,5,4,2,1}, sigma_4(20) = 160000 + 10000 + 625 + 256 + 16 + 1 = 170898, sigma_2(20) = 400 + 100 + 25 + 16 + 4 + 1 = 546; p = 170898/546 = 73 is prime, the 2nd term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2000 (terms 1..250 from Harry J. Smith)

Crossrefs

Cf. A000040, A001157, A001159, A066109, A066111, A066112.

Programs

Mathematica

Do[s=DivisorSigma[4, n]; z=DivisorSigma[2, n]; If[PrimeQ[s/z], Print[s/z]], {n, 1, 10000000}]
Select[Table[DivisorSigma[4,n]/DivisorSigma[2,n],{n,200000}],PrimeQ] (* Harvey P. Dale, Jan 31 2022 *)

PARI

{ n=0; for (m=1, 10^9, if (frac(f=sigma(m, 4)/sigma(m, 2)), next); if (isprime(f), write("b066110.txt", n++, " ", f); if (n==250, return)) ) } \\ Harry J. Smith, Feb 01 2010

Formula

Primes of the form A001159(A066109(k))/A001157(A066109(k)).