This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A066109 #28 Feb 25 2025 02:12:13
%S A066109 4,9,20,25,169,289,961,1849,3721,6889,11881,14641,15625,17161,52441,
%T A066109 57121,66049,69169,72361,96721,97969,117649,130321,196249,214369,
%U A066109 253009,326041,351649,358801,383161,410881,418609,426409,434281,491401
%N A066109 Numbers k such that sigma_4(k)/sigma_2(k) is prime.
%C A066109 Numbers k such that A001159(k)/A001157(k) is prime.
%C A066109 Except for the 3rd term 20, below 10000000 all the other terms are even powers of a prime. These primes are listed in A066111. It is not known whether other numbers similar to 20 exist or not.
%C A066109 20 is the only exception within the first 2000 terms. - _Amiram Eldar_, Feb 25 2025
%H A066109 Amiram Eldar, <a href="/A066109/b066109.txt">Table of n, a(n) for n = 1..2000</a> (terms 1..250 from Harry J. Smith)
%e A066109 For k = 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.
%t A066109 Do[s = DivisorSigma[4, n]; z = DivisorSigma[2, n]; If[PrimeQ[s/z], Print[{n, s, z, s/z}]], {n, 1, 10000000}]
%t A066109 Select[Range[500000],PrimeQ[DivisorSigma[4,#]/DivisorSigma[2,#]]&] (* _Harvey P. Dale_, May 02 2011 *)
%o A066109 (PARI) isok(k) = { my(f=sigma(k, 4)/sigma(k, 2)); !frac(f) && isprime(f) } \\ _Harry J. Smith_, Nov 16 2009
%Y A066109 Cf. A000040, A001157, A001159, A046871, A066111, A066112.
%K A066109 nonn
%O A066109 1,1
%A A066109 _Labos Elemer_, Dec 05 2001