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%I #23 Feb 24 2023 12:29:03
%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 472392,649800,734472,808992,995328,1143072,1190700,1254528,1529388,1685448,1960200,2056752
%N Powerful numbers (definition 1) sandwiched between twin primes.
%C Here we are considering powerful numbers defined in A001694.
%H Amiram Eldar, <a href="/A113839/b113839.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Donovan Johnson)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number</a>.
%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%e 72 = 2^3*3^2 is powerful 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 Intersection of A001694 and A014574.
%Y Cf. A001097.
%K nonn
%O 1,1
%A _Giovanni Resta_, Jan 24 2006
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