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 A195382 #20 Mar 15 2023 10:50:13
%S A195382 4,8,16,18,32,50,256,512,578,1458,2048,3362,4802,6962,8192,10082,
%T A195382 15842,20402,31250,34322,55778,57122,59858,167042,171698,293378,
%U A195382 524288,559682,916658,982802,1062882,1104098,1158242,1195058,1367858,1407842,1414562
%N A195382 Numbers such that the difference between the sum of the even divisors and the sum of the odd divisors is prime.
%C A195382 Note that these are all even numbers. The odd numbers, producing the negative of a prime, are all squares whose square roots are in A193070. - _T. D. Noe_, Sep 19 2011
%H A195382 Charles R Greathouse IV, <a href="/A195382/b195382.txt">Table of n, a(n) for n = 1..10000</a>
%e A195382 The divisors of 18 are { 1, 2, 3, 6, 9, 18}, and (2 + 6 + 18) - (1 + 3 + 9) = 13 is prime. Hence 18 is in the sequence.
%p A195382 with(numtheory):for n from 2 by 2 to 200 do:x:=divisors(n):n1:=nops(x):s1:=0:s2:=0:for m from 1 to n1 do:if irem(x[m],2)=1 then s1:=s1+x[m]:else s2:=s2+x[m]:fi:od: if type(s2-s1,prime)=true then printf(`%d, `,n): else fi:od:
%t A195382 f[n_] := Module[{d = Divisors[n], p}, p = Plus @@ Select[d, OddQ] - Plus @@ Select[d, EvenQ]; PrimeQ[p]]; Select[Range[2,1000000,2], f] (* _T. D. Noe_, Sep 19 2011 *)
%o A195382 (PARI) list(lim)=my(v=List(),t);forstep(n=3,sqrt(lim\2),2,if(isprime(s=sigma(n^2)),listput(v,2*n^2)));t=2;while((t*=2)<=lim,if(isprime(2*sigma(t/2)-1),listput(v,t)));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Sep 18 2011
%Y A195382 Subsequence of A088827.
%Y A195382 Cf. A002129, A113184.
%K A195382 nonn
%O A195382 1,1
%A A195382 _Michel Lagneau_, Sep 17 2011