A113839 Powerful numbers (definition 1) sandwiched between twin primes.

4, 72, 108, 432, 1152, 2592, 3528, 9000, 18252, 20808, 21600, 34848, 49392, 69192, 83232, 103968, 139968, 180000, 197568, 264600, 345600, 362952, 438048, 444528, 472392, 649800, 734472, 808992, 995328, 1143072, 1190700, 1254528, 1529388, 1685448, 1960200, 2056752

Offset

1,1

Comments

Here we are considering powerful numbers defined in A001694.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Donovan Johnson)

Eric Weisstein's World of Mathematics, Powerful Number.

Index entries for sequences related to powerful numbers.

Example

72 = 2^3*3^2 is powerful and 71 and 73 are twin primes, so 72 is in the sequence.

Mathematica

pwfQ[n_] := n == 1 || Min[Transpose[FactorInteger@n][[2]]] > 1; lst={}; Do[If[PrimeQ[n-1] && PrimeQ[n+1] && pwfQ[n], AppendTo[lst, n]], {n, 4, 2*10^6, 4}]; lst

Prog

(PARI) isA113839(n)=isprime(n-1)&&isprime(n+1)&&vecmax(factor(n)[, 2])>1 \\ Charles R Greathouse IV, Jun 29 2011

Crossrefs

Intersection of A001694 and A014574.

Cf. A001097.

Sequence in context: A128062 A336253 A227248 * A077112 A203537 A095385

Adjacent sequences: A113836 A113837 A113838 * A113840 A113841 A113842

Keyword

nonn,changed

Author

Giovanni Resta, Jan 24 2006

Status

approved