A360841 4-full numbers (A036967) sandwiched between twin primes.

2592, 139968, 995328, 37340352, 63700992, 99574272, 169869312, 414720000, 1399680000, 4076863488, 10871635968, 17714700000, 22781250000, 25312500000, 35888419872, 51840000000, 82012500000, 98802571392, 135304020000, 136136700000, 170749797552, 174960000000, 196730062848

Offset: 1

Author

Amiram Eldar, Feb 23 2023

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1520 (terms below 3*10^19)
• Eric Weisstein's World of Mathematics, Twin Primes.
• Wikipedia, Powerful number: Generalization.
• Index entries for sequences related to powerful numbers.

Crossrefs

Intersection of A014574 and A036967.

Subsequence of A113839 and A360840.

Programs

Mathematica

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

PARI

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