login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113839 Powerful(1) numbers sandwiched between twin primes. 2

%I

%S 4,72,108,432,1152,2592,3528,9000,18252,20808,21600,34848,49392,69192,

%T 83232,103968,139968,180000,197568,264600,345600,362952,438048,444528,

%U 472392,649800,734472,808992,995328,1143072,1190700,1254528,1529388

%N Powerful(1) numbers sandwiched between twin primes.

%C Here we are considering powerful numbers defined in A001694.

%H Donovan Johnson, <a href="/A113839/b113839.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number</a>

%e 72=2^3*3^2 is powerful(1) and 71 and 73 are twin primes, so 72 is in the sequence.

%t 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

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

%Y Cf. A001694, A001097.

%K nonn

%O 1,1

%A _Giovanni Resta_, Jan 24 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 06:52 EDT 2019. Contains 327119 sequences. (Running on oeis4.)