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.
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}
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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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 23 2023
EXTENSIONS
More terms from Bert Dobbelaere, Feb 24 2023
STATUS
approved