A378593 Number of squarefree k between consecutive powerful numbers (inclusive).

3, 3, 0, 5, 5, 1, 3, 3, 8, 8, 6, 5, 11, 6, 8, 2, 1, 11, 14, 17, 2, 11, 6, 11, 7, 20, 0, 22, 10, 10, 18, 6, 20, 6, 28, 9, 8, 9, 28, 30, 14, 17, 0, 32, 33, 12, 24, 12, 22, 37, 4, 3, 17, 16, 36, 24, 16, 3, 42, 44, 18, 4, 13, 11, 2, 45, 46, 29, 20, 48, 26, 22, 23

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) > A076446(n) for n > 1.

a(n) >= A240590(n).

Example

a(1) = 3 since {[1], 2, 3, [4]} has 3 squarefree numbers.
a(2) = 3 since {[4], 5, 6, 7, [8]} has 3 squarefree numbers.
a(3) = 0 since {[8], [9]} has no squarefree numbers.
a(4) = 5 since between 9 and 16, {10, 11, 13, 14, 15} are squarefree.
a(5) = 5 since between 16 and 25, {17, 19, 21, 22, 23} are squarefree, etc.

Mathematica

With[{nn = 2^12},
  s = Union@ Flatten@ Table[a^2*b^3, {b, Surd[nn, 3]}, {a, Sqrt[nn/b^3]}];  Table[Count[Range[s[[i]], s[[i + 1]]], _?SquareFreeQ], {i, Length[s] - 1}]

Crossrefs

Cf. A001694, A005117, A076446, A240590.

Sequence in context: A128046 A102899 A353327 * A072689 A021972 A193451

Adjacent sequences: A378590 A378591 A378592 * A378594 A378595 A378596

Keyword

nonn

Author

Michael De Vlieger, Dec 09 2024

Status

approved