%I #14 Feb 27 2023 05:27:36

%S 2592,139968,995328,37340352,63700992,99574272,169869312,414720000,

%T 1399680000,4076863488,10871635968,17714700000,22781250000,

%U 25312500000,35888419872,51840000000,82012500000,98802571392,135304020000,136136700000,170749797552,174960000000,196730062848

%N 4-full numbers (A036967) sandwiched between twin primes.

%H Amiram Eldar, <a href="/A360841/b360841.txt">Table of n, a(n) for n = 1..1520</a> (terms below 3*10^19)

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Powerful_number#Generalization">Powerful number: Generalization</a>.

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

%e 2592 = 2^5 * 3^4 is a term since it is 4-full and 2591 and 2593 are twin primes.

%t Select[6*Range[2*10^5], PrimeQ[# - 1] && PrimeQ[# + 1] && Min[FactorInteger[#][[;; , 2]]] > 3 &]

%o (PARI) is(n) = isprime(n-1) && isprime(n+1) && vecmin(factor(n)[,2]) > 3;

%Y Intersection of A014574 and A036967.

%Y Subsequence of A113839 and A360840.

%K nonn

%O 1,1

%A _Amiram Eldar_, Feb 23 2023