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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 05 2001
STATUS
approved