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A336025 Numbers m providing record values for the proportion of nonsquarefree integers in the interval [1, m]. 1
4, 9, 20, 25, 27, 28, 172, 176 (list; graph; refs; listen; history; text; internal format)



Also, numbers providing record low values for the proportion of squarefree integers.

The proportion of nonsquarefree integers approaches 1-6/Pi^2. For low values of m the proportion in [1, m] tends to be lower, since squares appear late. But values of m for which the ratio in the interval [1, m] is larger than the limit value do exist. The first such one is 28. Therefore this sequence is finite and it can be proved that 176 is indeed its last term. The proportion of nonsquarefree numbers in [1, 176] is 70/176 = 0.397727272... and that of squarefree ones is 0.6022727...


Table of n, a(n) for n=1..8.


Up to m = 9 there are 3 numbers which are divisible by some square: 4, 8 and 9, for a proportion of 3/9 = 1/3. No interval [1, k] for k < 9 has a ratio as high, so 9 is in the sequence.


Cf. A005117, A013929, A173143, A057627.

Sequence in context: A023377 A187408 A211055 * A308482 A136769 A115075

Adjacent sequences:  A336022 A336023 A336024 * A336026 A336027 A336028




Javier Múgica, Jul 05 2020



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Last modified March 5 15:22 EST 2021. Contains 341825 sequences. (Running on oeis4.)