cp's OEIS Frontend

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

%I A065514 #21 Dec 04 2024 21:24:54
%S A065514 1,2,4,5,9,11,16,17,19,27,29,32,37,41,43,49,53,59,64,67,71,73,81,83,
%T A065514 89,97,101,103,107,109,125,128,131,137,139,149,151,157,163,169,173,
%U A065514 179,181,191,193,197,199,211,223,227,229,233,239,243,256,257,263,269,271
%N A065514 Largest power of a prime < prime(n).
%t A065514 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 *)
%o A065514 (Python)
%o A065514 from sympy import factorint, prime
%o A065514 def A065514(n): return next(filter(lambda m:len(factorint(m))<=1, range(prime(n)-1,0,-1))) # _Chai Wah Wu_, Oct 25 2024
%Y A065514 Starting with n instead of prime(n) gives A031218 (A377282, A377782).
%Y A065514 The squarefree version is A112925 (A070321, A378038).
%Y A065514 The opposite squarefree version is A112926 (A378037, restriction of A067535).
%Y A065514 Difference from prime(n) is A377289 (restriction of A276781, opposite A377281).
%Y A065514 First differences are A377781.
%Y A065514 The nonsquarefree version is A378032 (A377783 (restriction of A378033), A378034, A378040).
%Y A065514 The perfect power version is A378035.
%Y A065514 A000015 gives the least prime power >= n, differences A377780.
%Y A065514 A000040 lists the primes, differences A001223.
%Y A065514 A000961 and A246655 list the prime powers, differences A057820.
%Y A065514 A024619 and A361102 list the non prime powers, differences A375708 and A375735.
%Y A065514 A345531 gives the least prime power > prime(n), differences A377703.
%Y A065514 Prime powers between primes: A053607, A080101, A304521, A366833, A377057, A377286.
%Y A065514 Cf. A014234, A053707, A065890, A376597, A377051, A378249, A378252.
%K A065514 nonn
%O A065514 1,2
%A A065514 _Reinhard Zumkeller_, Nov 27 2001
%E A065514 Name edited (1 is technically not a prime power even though it is a power of a prime) by _Gus Wiseman_, Dec 03 2024.