A115560 Twin prime pairs k-1 and k+1 such that the squares of both are present in A115557.

11, 13, 29, 31, 197, 199, 239, 241, 419, 421, 659, 661, 881, 883, 1019, 1021, 1061, 1063, 1481, 1483, 1877, 1879, 3167, 3169, 3821, 3823, 4019, 4021, 4049, 4051, 4787, 4789, 6359, 6361, 7589, 7591, 9437, 9439, 13691, 13693, 14447, 14449, 14627, 14629, 16451, 16453

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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.

Mathematica

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]

Prog

(PARI) isok(n) = issquare(n) && (sigma(numdiv(n)) == numdiv(sigma(n))); \\ A115557
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

Crossrefs

Cf. A000005, A000203, A076360, A076361, A062068, A062069, A115557, A115558, A115559.

Sequence in context: A140567 A232880 A117314 * A045466 A158759 A107645

Adjacent sequences: A115557 A115558 A115559 * A115561 A115562 A115563

Keyword

nonn

Author

Labos Elemer, Jan 25 2006

Extensions

More terms from Amiram Eldar, Jul 17 2019

Status

approved