A080102 Smallest prime power in all composite numbers between n-th prime and next prime, a(n) = 1 if no such prime power exists.

4, 1, 8, 1, 16, 1, 1, 25, 1, 32, 1, 1, 1, 49, 1, 1, 64, 1, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 121, 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 32749 = A000040(3512) and 32771 = A000040(3513): 32761 = 181^2 and 32768 = 2^15, therefore a(3512) = 32761, A080103(3512) = 32768 and A080101(3512) = 2.
		

Links

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

Crossrefs

Cf. A080101, A080103, A025475, A000961.

Programs

Mathematica

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