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%I #12 Jun 28 2024 13:59:20
%S 2,3,4,5,4,7,8,9,8,11,8,13,8,9,16,17,16,19,16,9,16,23,16,25,16,27,16,
%T 29,16,31,32,27,32,25,32,37,32,27,32,41,32,43,32,27,32,47,32,49,32,27,
%U 32,53,32,25,32,27,32,59,32,61,32,27,64,25,64,67,64,27,64
%N a(n) = p^floor(log_p n) for p = A020639(n).
%C Let p = A020639(n), then a(n) is the largest power p^m that does not exceed n.
%C For n in A024619, a(n) neither divides nor is coprime to n.
%H Michael De Vlieger, <a href="/A373735/b373735.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = n for powers of primes n = p^m, m > 0.
%F a(n) = A020639(n)^A280363(n), therefore a(n) is in A246655.
%F a(n) is a power of 2 for even n.
%e a(2) = 2 since lpf(2) = 2, and 2^1 = 2 is the largest power of 2 that does not exceed 2.
%e a(6) = 4 since lpf(6) = 2, and 2^2 = 4 is the largest power of 2 that does not exceed 6.
%e a(15) = 9 since lpf(15) = 3, and 3^2 = 9 is the largest power of 3 that does not exceed 15, etc.
%t Table[#^Floor@ Log[#, n] &[FactorInteger[n][[1, 1]] ], {n, 2, 120}]
%o (PARI) a(n) = my(p=vecmin(factor(n)[,1])); p^logint(n, p); \\ _Michel Marcus_, Jun 18 2024
%Y Cf. A000079, A020639, A024619, A246655, A280363.
%K nonn,easy
%O 2,1
%A _Michael De Vlieger_, Jun 18 2024