A360843 6-full numbers (A069493) sandwiched between twin primes.

139968, 98802571392, 174960000000, 889223142528, 1594323000000, 2348273369088, 19144761127488, 28697814000000, 56358560858112, 84537841287168, 150289495621632, 186624000000000, 328341017826432, 369056250000000, 392147405854848, 578415690713088, 597871125000000

Offset: 1

Author

Amiram Eldar, Feb 23 2023

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..74 (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 A069493.

Subsequence of A113839, A360840, A360841 and A360842.

Programs

Mathematica

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

PARI

is(n) = isprime(n-1) && isprime(n+1) && vecmin(factor(n)[,2]) > 5;