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%I #13 Jan 31 2022 17:42:37
%S 13,73,313,601,28393,83233,922561,3416953,13842121,47451433,141146281,
%T 212601841,234750601,294482761,2750006041,3262751521,4362404353,
%U 4784281393,5236041961,9354855121,9597826993,13564461457,16936647121
%N Primes of form sigma_4(n)/sigma_2(n), arising in A066109.
%H Harry J. Smith, <a href="/A066110/b066110.txt">Table of n, a(n) for n=1..250</a>
%F Primes of form A001159(A066109(n))/A001157(A066109(n)).
%e 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.
%t 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.
%t Select[Table[DivisorSigma[4,n]/DivisorSigma[2,n],{n,200000}],PrimeQ] (* _Harvey P. Dale_, Jan 31 2022 *)
%o (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
%Y Cf. A000040, A001157, A001159, A066109-A066113.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 05 2001
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