A373735 a(n) = p^floor(log_p n) for p = A020639(n).

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, 29, 16, 31, 32, 27, 32, 25, 32, 37, 32, 27, 32, 41, 32, 43, 32, 27, 32, 47, 32, 49, 32, 27, 32, 53, 32, 25, 32, 27, 32, 59, 32, 61, 32, 27, 64, 25, 64, 67, 64, 27, 64

Offset

2,1

Comments

Let p = A020639(n), then a(n) is the largest power p^m that does not exceed n.

For n in A024619, a(n) neither divides nor is coprime to n.

Links

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Formula

a(n) = n for powers of primes n = p^m, m > 0.

a(n) = A020639(n)^A280363(n), therefore a(n) is in A246655.

a(n) is a power of 2 for even n.

Example

a(2) = 2 since lpf(2) = 2, and 2^1 = 2 is the largest power of 2 that does not exceed 2.
a(6) = 4 since lpf(6) = 2, and 2^2 = 4 is the largest power of 2 that does not exceed 6.
a(15) = 9 since lpf(15) = 3, and 3^2 = 9 is the largest power of 3 that does not exceed 15, etc.

Mathematica

Table[#^Floor@ Log[#, n] &[FactorInteger[n][[1, 1]] ], {n, 2, 120}]

Prog

(PARI) a(n) = my(p=vecmin(factor(n)[, 1])); p^logint(n, p); \\ Michel Marcus, Jun 18 2024

Crossrefs

Cf. A000079, A020639, A024619, A246655, A280363.

Sequence in context: A349958 A058084 A074882 * A377487 A273284 A079867

Adjacent sequences: A373732 A373733 A373734 * A373736 A373737 A373738

Keyword

nonn,easy

Author

Michael De Vlieger, Jun 18 2024

Status

approved