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A000015 Smallest prime power >= n.

%I A000015 #78 Feb 16 2025 08:32:18
%S A000015 1,2,3,4,5,7,7,8,9,11,11,13,13,16,16,16,17,19,19,23,23,23,23,25,25,27,
%T A000015 27,29,29,31,31,32,37,37,37,37,37,41,41,41,41,43,43,47,47,47,47,49,49,
%U A000015 53,53,53,53,59,59,59,59,59,59,61,61,64,64,64,67,67,67,71,71,71,71,73
%N A000015 Smallest prime power >= n.
%C A000015 The length of the m-th run of {a(n)} is the length of the (m-1)-st run of A031218 for m > 1. - _Colin Linzer_, Mar 08 2024
%H A000015 David W. Wilson, <a href="/A000015/b000015.txt">Table of n, a(n) for n = 1..10000</a>
%H A000015 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePower.html">Prime Power</a>.
%F A000015 a(A110654(n+1)) = A188666(n). - _Reinhard Zumkeller_, Apr 25 2011, corrected by _M. F. Hasler_, Jul 25 2015
%F A000015 a(n) = A188666(2n-1). - _M. F. Hasler_, Jul 25 2015
%p A000015 N:= 1000: # to get all terms <= N
%p A000015 Primes:= select(isprime,{$1..N}):
%p A000015 PPs:= {1} union Primes:
%p A000015 for k from 1 to ilog2(N) do
%p A000015    PPs:= PPs union map(`^`, select(`<=`,Primes, floor(N^(1/k))),k)
%p A000015 od:
%p A000015 PPs:= sort(convert(PPs,list)):
%p A000015 1, seq(PPs[i]$(PPs[i]-PPs[i-1]), i=2..nops(PPs)); # _Robert Israel_, Jul 23 2015
%t A000015 Insert[Table[m:=n;While[Not[Length[FactorInteger[m]]==1],m++ ];m,{n,2,100}], 1, 1] (* _Stefan Steinerberger_, Apr 17 2006 *)
%t A000015 a[n_] := NestWhile[# + 1 &, n, Not@*PrimePowerQ]; (* _Matthew House_, Jul 14 2015, v6.0+ *)
%t A000015 a[ n_] := If[ n < 2, Boole[n == 1], Module[{m = n}, While[ ! PrimePowerQ[ m], m++]; m]]; (* _Michael Somos_, Mar 06 2018 *)
%t A000015 a[ n_] := If[ n < 1, 0, Module[{m = n}, While[ Length[ FactorInteger @ m ] != 1, m++]; m]]; (* _Michael Somos_, Mar 06 2018 *)
%o A000015 (PARI) {a(n) = if( n<1, 0, while(matsize(factor(n))[1]>1, n++); n)}; /* _Michael Somos_, Jul 16 2002 */
%o A000015 (PARI) a(n)=if(n>1,while(!isprimepower(n),n++));n \\ _Charles R Greathouse IV_, Feb 01 2013
%o A000015 (Sage) [next_prime_power(n) for n in range(72)]  # _Zerinvary Lajos_, Jun 13 2009
%o A000015 (Haskell)
%o A000015 a000015 n = a000015_list !! (n-1)
%o A000015 a000015_list = 1 : concat
%o A000015    (zipWith(\pp qq -> replicate (fromInteger (pp - qq)) pp)
%o A000015            (tail a000961_list) a000961_list)
%o A000015 -- _Reinhard Zumkeller_, Nov 17 2011, Apr 25 2011
%o A000015 (Python)
%o A000015 from itertools import count
%o A000015 from sympy import factorint
%o A000015 def A000015(n): return next(filter(lambda m:len(factorint(m))<=1, count(n))) # _Chai Wah Wu_, Oct 25 2024
%Y A000015 Cf. A000961, A031218.
%K A000015 nonn,easy
%O A000015 1,2
%A A000015 _N. J. A. Sloane_
%E A000015 More terms from _Michael Somos_, Jul 16 2002