A065514 Largest power of a prime < prime(n).

1, 2, 4, 5, 9, 11, 16, 17, 19, 27, 29, 32, 37, 41, 43, 49, 53, 59, 64, 67, 71, 73, 81, 83, 89, 97, 101, 103, 107, 109, 125, 128, 131, 137, 139, 149, 151, 157, 163, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 243, 256, 257, 263, 269, 271

Offset: 1

Author

Reinhard Zumkeller, Nov 27 2001

Keywords

• nonn

Crossrefs

Starting with n instead of prime(n) gives A031218 (A377282, A377782).

The squarefree version is A112925 (A070321, A378038).

The opposite squarefree version is A112926 (A378037, restriction of A067535).

Difference from prime(n) is A377289 (restriction of A276781, opposite A377281).

First differences are A377781.

The nonsquarefree version is A378032 (A377783 (restriction of A378033), A378034, A378040).

The perfect power version is A378035.

A000015 gives the least prime power >= n, differences A377780.

A000040 lists the primes, differences A001223.

A000961 and A246655 list the prime powers, differences A057820.

A024619 and A361102 list the non prime powers, differences A375708 and A375735.

A345531 gives the least prime power > prime(n), differences A377703.

Prime powers between primes: A053607, A080101, A304521, A366833, A377057, A377286.

Cf. A014234, A053707, A065890, A376597, A377051, A378249, A378252.

Programs

Mathematica

lpp[n_]:=Module[{k=n-1},While[!PrimePowerQ[k],k--];k]; Join[{1},Table[ lpp[ n],{n,Prime[Range[2,60]]}]] (* Harvey P. Dale, Nov 24 2018 *)

Python

from sympy import factorint, prime
def A065514(n): return next(filter(lambda m:len(factorint(m))<=1, range(prime(n)-1,0,-1))) # Chai Wah Wu, Oct 25 2024

Extensions

Name edited (1 is technically not a prime power even though it is a power of a prime) by Gus Wiseman, Dec 03 2024.