A377487 - OEIS

%I #9 Nov 01 2024 21:08:47

%S 1,2,3,4,5,4,7,8,9,8,11,9,13,8,9,16,17,16,19,16,9,16,23,16,25,16,27,

%T 16,29,27,31,32,27,32,25,32,37,32,27,32,41,32,43,32,27,32,47,32,49,32,

%U 27,32,53,32,25,49,27,32,59,32,61,32,49,64,25,64,67,64,27

%N a(n) = largest power p^k <= n for prime p among prime factors of n.

%C a(1) = 1 by convention.

%C a(n) is the largest prime power in row n of A162306.

%H Michael De Vlieger, <a href="/A377487/b377487.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A377487/a377487.png">Log log scatterplot a(n)</a>, n = 1..2^20.

%F a(p) = p for prime p.

%F a(p^k) = p^k.

%e a(6) = 4 since 6 = 2*3, the largest powers of these numbers that do not exceed 6 are 4 and 3 respectively, and 4 is the largest.

%e a(10) = 8 since 10 = 2*5, with 2^3 = 8 and 5^1 = 5 the largest powers of each respectively, and 8 is the largest.

%e a(30) = 27 since 30 = 2*3*5, with 2^4 = 16, 3^3 = 27, and 5^2 = 25 the largest powers of each respectively; 27 is the largest, etc.

%t {1}~Join~Table[Max@ Map[#^Floor@ Log[#, n] &, FactorInteger[n][[All, 1]]], {n, 2, 120}]

%o (Python)

%o from sympy import integer_log, primefactors

%o def A377487(n): return max((p**integer_log(n,p)[0] for p in primefactors(n)), default=1) # _Chai Wah Wu_, Nov 01 2024

%Y Cf. A162306, A246655.

%K nonn,easy

%O 1,2

%A _Michael De Vlieger_, Oct 29 2024