|
%I #13 Jul 17 2019 10:56:11
%S 11,13,29,31,197,199,239,241,419,421,659,661,881,883,1019,1021,1061,
%T 1063,1481,1483,1877,1879,3167,3169,3821,3823,4019,4021,4049,4051,
%U 4787,4789,6359,6361,7589,7591,9437,9439,13691,13693,14447,14449,14627,14629,16451,16453
%N Twin prime pairs k-1 and k+1 such that the squares of both are present in A115557.
%H Amiram Eldar, <a href="/A115560/b115560.txt">Table of n, a(n) for n = 1..10000</a>
%F The commutator [sigma, tau] is zero and a(n) is the square root of special prime solutions. These solutions are twin primes. Both twins are displayed.
%t ta={{0}};tb={{0}}; Do[s=DivisorSigma[1,DivisorSigma[0,n]]; s1=DivisorSigma[0,DivisorSigma[1,n]]; If[Equal[s-s1,0]&&IntegerQ[Sqrt[n]&&PrimeQ[Sqrt[n]]],Print[n]; ta=Append[ta,n];tb=Append[tb,Sqrt[n]]],{n,1,100000000}] ta=Delete[ta,1];tb=Delete[tb,1];ni=Intersection[tb,2+tb]; Union[ni,ni-2]
%o (PARI) isok(n) = issquare(n) && (sigma(numdiv(n)) == numdiv(sigma(n))); \\ A115557
%o lista(nn) = {forprime(p=2, nn, if (isprime(p+2) && isok(p^2) && isok((p+2)^2), print1(p, ", ", p+2, ", ")););} \\ _Michel Marcus_, Jul 17 2019
%Y Cf. A000005, A000203, A076360, A076361, A062068, A062069, A115557, A115558, A115559.
%K nonn
%O 1,1
%A _Labos Elemer_, Jan 25 2006
%E More terms from _Amiram Eldar_, Jul 17 2019
|
