login
A322449
Numbers whose prime factorization contains only composite exponents.
5
1, 16, 64, 81, 256, 512, 625, 729, 1024, 1296, 2401, 4096, 5184, 6561, 10000, 11664, 14641, 15625, 16384, 19683, 20736, 28561, 32768, 38416, 40000, 41472, 46656, 50625, 59049, 65536, 82944, 83521, 104976, 117649, 130321, 153664, 160000, 186624, 194481, 234256
OFFSET
1,2
COMMENTS
Differs from A117453 first at n = 13: a(13) = 5184 = 2^6 * 3^4, A117453(13) = 6561 = 3^8.
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k in A002808} 1/p^k) = 1.1028952548... . - Amiram Eldar, Jul 02 2022
EXAMPLE
5184 = 2^6 * 3^4 is a term because all exponents are composite numbers.
1 is a term, because it has no prime factorization, and "the empty set has every property". - N. J. A. Sloane, Aug 25 2024
MATHEMATICA
Join[{1}, Select[Range[250000], AllTrue[FactorInteger[#][[;; , 2]], CompositeQ]&]] (* Harvey P. Dale, Aug 25 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 08 2018
STATUS
approved