A360844 a(n) is the least k-full number that is sandwiched between twin primes.

4, 432, 2592, 139968, 139968, 174960000000, 56358560858112, 84537841287168, 578415690713088, 578415690713088, 1141260857376768, 61628086298345472, 61628086298345472, 61628086298345472, 322850407500000000000000000000, 322850407500000000000000000000, 62518864539857068333550694039552

Offset

2,1

Comments

k-full number is a number m such that if a prime p divides m then so does p^k. All the exponents in the canonical prime factorization of a k-full number are not smaller than k.

a(2)-a(15) are the terms below 3*10^19. Except for a(7) = 174960000000, they are all 3-smooth numbers (A003586, and thus they are terms of A027856). Are there other terms that are not 3-smooth?

a(168) = 2^176 * 3^173 * 7^168 is the first term that is not 5-smooth. - Bert Dobbelaere, Feb 24 2023

Links

Bert Dobbelaere, Table of n, a(n) for n = 2..200

Eric Weisstein's World of Mathematics, Twin Primes.

Wikipedia, Powerful number: Generalization.

Index entries for sequences related to powerful numbers.

Example

The first 3 terms, their factorizations and the corresponding twin primes are:
  n |   a(n)  prime factorization  A051904(a(n))  {a(n)-1, a(n)+1}
  ----------------------------------------------------------------
  2 |     4                  2^2              2             {3, 5}
  3 |   432            2^4 * 3^3              3         {431, 433}
  4 |  2592            2^5 * 3^4              4       {2591, 2593}

Crossrefs

Cf. A001097, A001694, A014574, A036966, A036967, A069492, A069493.

Cf. A113839, A360840, A360841, A360842, A360843.

Cf. A027856, A003586, A051904.

Sequence in context: A036771 A201980 A080321 * A264469 A369395 A172858

Adjacent sequences: A360841 A360842 A360843 * A360845 A360846 A360847

Keyword

nonn

Author

Amiram Eldar, Feb 23 2023

Extensions

More terms from Bert Dobbelaere, Feb 24 2023

Status

approved