A360842 5-full numbers (A069492) sandwiched between twin primes.

139968, 995328, 63700992, 4076863488, 17714700000, 82012500000, 98802571392, 174960000000, 445240556352, 641194278912, 889223142528, 1059917571072, 1594323000000, 1663012435968, 2348273369088, 3333709317312, 5717741400000, 16260080320512, 19144761127488, 28697814000000

Offset: 1

Author

Amiram Eldar, Feb 23 2023

Keywords

• nonn

Examples

			139968 = 2^6 * 3^7 is a term since it is 5-full and 139967 and 139969 are twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..250 (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 A069492.

Subsequence of A113839, A360840 and A360841.

Programs

Mathematica

Select[6*Range[2*10^5], PrimeQ[# - 1] && PrimeQ[# + 1] && Min[FactorInteger[#][[;; , 2]]] > 4 &]

PARI

is(n) = isprime(n-1) && isprime(n+1) && vecmin(factor(n)[,2]) > 4;