A336594 Numbers k such that k/A008835(k) is cubefree but not squarefree (A067259), where A008835(k) is the largest 4th power dividing k.

4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, 63, 64, 68, 75, 76, 84, 90, 92, 98, 99, 100, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 164, 169, 171, 172, 175, 180, 188, 192, 196, 198, 204, 207, 212, 220, 225, 228, 234, 236, 242, 244

Offset

1,1

Comments

Numbers such that at least one of the exponents in their prime factorization is of the form 4*m + 2, and none are of the form 4*m + 3.

The asymptotic density of this sequence is zeta(4) * (1/zeta(3) - 1/zeta(2)) = Pi^4/(90*zeta(3)) - Pi^2/15 = 0.2424190509... (Cohen, 1963).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eckford Cohen, Arithmetical Notes, XIII. A Sequal to Note IV, Elemente der Mathematik, Vol. 18 (1963), pp. 8-11.

Example

4 is a term since the largest 4th power dividing 4 is 1, and 4/1 = 4 = 2^2 is cubefree but not squarefree.
64 is a term since the largest 4th power dividing 64 is 16, and 64/16 = 4 = 2^2 is cubefree but not squarefree.

Mathematica

Select[Range[250], Max[Mod[FactorInteger[#][[;; , 2]], 4]] == 2 &]

Crossrefs

Cf. A002117, A008835, A013661, A013662, A067259, A182358.

Complement of A336593 within A252849.

A030140 is a subsequence.

Sequence in context: A059269 A369209 A081619 * A304365 A038109 A067259

Adjacent sequences: A336591 A336592 A336593 * A336595 A336596 A336597

Keyword

nonn

Author

Amiram Eldar, Jul 26 2020

Status

approved