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Largest prime power <= n.
19

%I #33 Oct 25 2024 13:13:36

%S 1,2,3,4,5,5,7,8,9,9,11,11,13,13,13,16,17,17,19,19,19,19,23,23,25,25,

%T 27,27,29,29,31,32,32,32,32,32,37,37,37,37,41,41,43,43,43,43,47,47,49,

%U 49,49,49,53,53,53,53,53,53,59,59,61,61,61,64,64,64,67,67,67,67,71,71

%N Largest prime power <= n.

%C The length of the m-th run of {a(n)} is the length of the (m+1)-st run of A000015 for m > 1. - _Colin Linzer_, Mar 08 2024

%H Reinhard Zumkeller, <a href="/A031218/b031218.txt">Table of n, a(n) for n = 1..10000</a>

%H B. Dearden, J. Iiams, and J. Metzger, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Dearden/dearden4.html">Rumor Arrays</a>, Journal of Integer Sequences, 16 (2013), #13.9.3.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>

%o (PARI) a(n)=if(n<1,0, while(matsize(factor(n))[1]>1,n--); n)

%o (Haskell)

%o a031218 n = last $ takeWhile (<= n) a000961_list

%o -- _Reinhard Zumkeller_, Apr 25 2011

%o (Python)

%o from sympy import factorint

%o def A031218(n): return next(filter(lambda m:len(factorint(m))<=1, range(n,0,-1))) # _Chai Wah Wu_, Oct 25 2024

%Y Cf. A000015, A000961.

%K nonn,easy,changed

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Erich Friedman_