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A373735
a(n) = p^floor(log_p n) for p = A020639(n).
1
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
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
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Jun 18 2024
STATUS
approved