A360840 3-full numbers (A036966) sandwiched between twin primes.

432, 2592, 139968, 444528, 472392, 995328, 3456000, 5174928, 6561000, 10125000, 15552000, 15804072, 17496000, 25299648, 28449792, 37340352, 54675000, 63700992, 85957848, 88723728, 99574272, 120891312, 144027072, 169869312, 177147000, 197413632, 253125000, 259308000

Offset: 1

Author

Amiram Eldar, Feb 23 2023

Keywords

• nonn

Examples

			432 = 2^4 * 3^3 is a term since it is 3-full and 431 and 433 are twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• 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 A036966.

Subsequence of A113839.

Programs

Mathematica

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

PARI

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