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 A096847 #29 Feb 14 2025 03:38:35
%S A096847 3,4,8,36,100,128,324,400,1296,1600,1936,2116,3364,4356,10404,11236,
%T A096847 20736,22500,26244,27556,28900,30976,38416,40000,52900,53824,57600,
%U A096847 60516,88804,93636,107584,108900,115600,123904,125316,129600,211600,215296,220900,256036
%N A096847 Numbers k such that A094471(k) is prime.
%C A096847 Old name was "Solutions to {A094471[x]=prime} that is to {x; x*tau[x]-sigma[x]=prime}."
%C A096847 All terms after the first are even, because A094471(n) is even if n is odd. The first term == 2 (mod 4) is a(135) = 9653618. - _Robert Israel_, Nov 11 2015
%C A096847 Except for 3, all the terms are either even squares or twice squares. - _Amiram Eldar_, Feb 14 2025
%H A096847 Amiram Eldar, <a href="/A096847/b096847.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..100 from Harvey P. Dale)
%e A096847 8 is a term since 8*tau(8) - sigma(8) = 8*4 - 15 = 32 - 15 = 17 is a prime.
%p A096847 A094471:= n -> n*numtheory:-tau(n) - numtheory:-sigma(n):
%p A096847 select(t -> isprime(A094471(t)), 2*[3/2,$1..10^6]); # _Robert Israel_, Nov 11 2015
%t A096847 Do[s=n*DivisorSigma[0, n]-DivisorSigma[1, n]; If[PrimeQ[s], Print[{n, s}]; ta[[u]]=n; tb[[u]]=s; u=u+1], {n, 1, 1000000}]; ta
%t A096847 Select[Range[215000],PrimeQ[# DivisorSigma[0,#]-DivisorSigma[1,#]]&] (* _Harvey P. Dale_, Dec 07 2021 *)
%t A096847 q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; PrimeQ[n * Times @@ (e + 1) - Times @@ ((p^(e + 1) - 1)/(p - 1))]]; seq[lim_] := Module[{m1 = Floor[Sqrt[lim/2]], m2 = Floor[Sqrt[lim]/2]}, Join[{3}, Union[Select[2*Range[m1]^2, q], Select[4*Range[m2]^2, q]]]]; seq[220000] (* _Amiram Eldar_, Feb 14 2025 *)
%o A096847 (PARI) isok(n) = isprime(n*numdiv(n)-sigma(n)); \\ _Michel Marcus_, Nov 12 2015
%o A096847 (PARI) isok(k) = if(k % 2, k == 3, if(!issquare(k) && !issquare(2*k), 0, my(f = factor(k)); isprime(k * numdiv(f) - sigma(f)))); \\ _Amiram Eldar_, Feb 14 2025
%Y A096847 Cf. A000005 (tau), A000203 (sigma), A094471, A096848.
%K A096847 nonn
%O A096847 1,1
%A A096847 _Labos Elemer_, Jul 15 2004
%E A096847 Name modified by _Tom Edgar_, Nov 12 2015