A080103 Greatest prime power in all composite numbers between n-th prime and next prime, a(n) = 1 if no such prime power exists.

4, 1, 9, 1, 16, 1, 1, 27, 1, 32, 1, 1, 1, 49, 1, 1, 64, 1, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 125, 128, 1, 1, 1, 1, 1, 1, 1, 169, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 243, 256, 1, 1, 1, 1, 1, 1, 289, 1, 1, 1, 1, 1, 1, 343, 1, 1, 1, 361, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Reinhard Zumkeller, Jan 28 2003

Keywords

• nonn

Examples

			There are two prime powers between 7 = A000040(4) and 11 = A000040(5): 8 = 2^3 and 9 = 3^2, therefore a(4) = 9, A080102(4) = 8 and A080101(4) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A080101, A080102, A025475, A000961.

Programs

Mathematica

a[n_] := SelectFirst[Range[Prime[n + 1] - 1, Prime[n] + 1, -1], PrimePowerQ, 1]; Array[a, 100, 2] (* Amiram Eldar, Mar 26 2025 *)