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

Author

Giovanni Resta, Jan 24 2006

Keywords

• nonn

Comments

Here we are considering powerful numbers defined in A001694.

Examples

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

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.

Crossrefs

Intersection of A001694 and A014574.

Cf. A001097.

Programs

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

PARI

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