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A115560 Twin prime pairs k-1 and k+1 such that the squares of both are present in A115557. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 23:38 EDT 2020. Contains 336279 sequences. (Running on oeis4.)