A066109 Numbers n such that sigma_4(n)/sigma_2(n) is prime.

4, 9, 20, 25, 169, 289, 961, 1849, 3721, 6889, 11881, 14641, 15625, 17161, 52441, 57121, 66049, 69169, 72361, 96721, 97969, 117649, 130321, 196249, 214369, 253009, 326041, 351649, 358801, 383161, 410881, 418609, 426409, 434281, 491401

Offset

1,1

Comments

Except for 3rd term 20, below 10000000 all other entries are even powers of a prime. These primes are listed in A066111. It is not known if other numbers similar to 20 exist or not.

Links

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

Formula

n such that A001159(n)/A001157(n) is prime.

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.

Mathematica

Do[s = DivisorSigma[4, n]; z = DivisorSigma[2, n]; If[PrimeQ[s/z], Print[{n, s, z, s/z}]], {n, 1, 10000000}]
Select[Range[500000], PrimeQ[DivisorSigma[4, #]/DivisorSigma[2, #]]&] (* Harvey P. Dale, May 02 2011 *)

Prog

(PARI) { n=0; for (m=1, 10^9, if (frac(f=sigma(m, 4)/sigma(m, 2)), next); if (isprime(f), write("b066109.txt", n++, " ", m); if (n==250, return)) ) } \\ Harry J. Smith, Nov 16 2009

Crossrefs

Cf. A000040, A001157, A001159.

Sequence in context: A288104 A053807 A327238 * A030734 A368587 A212101

Adjacent sequences: A066106 A066107 A066108 * A066110 A066111 A066112

Keyword

nonn

Author

Labos Elemer, Dec 05 2001

Status

approved