A066110 Primes of form sigma_4(n)/sigma_2(n), 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

1,1

Links

Harry J. Smith, Table of n, a(n) for n=1..250

Formula

Primes of form A001159(A066109(n))/A001157(A066109(n)).

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A001157, A001159, A066109-A066113.

Sequence in context: A143008 A107963 A006230 * A020527 A146618 A220414

Adjacent sequences: A066107 A066108 A066109 * A066111 A066112 A066113

Keyword

nonn

Author

Labos Elemer, Dec 05 2001

Status

approved