A182358 -id:A182358 - cp's OEIS frontend

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

Amiram Eldar, Jul 26 2020

nonn

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).

			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.

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.

Cf. A002117, A008835, A013661, A013662, A067259, A182358.
Complement of A336593 within A252849.
A030140 is a subsequence.

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

cp's OEIS Frontend

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

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