A322449 Numbers whose prime factorization contains only composite exponents.

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

Author

Alois P. Heinz, Dec 08 2018

Keywords

• nonn

Comments

Differs from A117453 first at n = 13: a(13) = 5184 = 2^6 * 3^4, A117453(13) = 6561 = 3^8.

Examples

			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
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A117453, A322448.

Programs

Mathematica

Join[{1},Select[Range[250000],AllTrue[FactorInteger[#][[;;,2]],CompositeQ]&]] (* Harvey P. Dale, Aug 25 2024 *)

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