A336593 Numbers k such that k/A008835(k) is cubeful (A036966), where A008835(k) is the largest 4th power dividing k.

8, 24, 27, 40, 54, 56, 72, 88, 104, 108, 120, 125, 128, 135, 136, 152, 168, 184, 189, 200, 216, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 343, 344, 351, 360, 375, 376, 378, 384, 392, 408, 424, 432, 440, 456, 459, 472, 488, 500, 504, 513, 520, 536, 540

Offset: 1

Author

Amiram Eldar, Jul 26 2020

Keywords

• nonn

Comments

Numbers such that at least one of the exponents in their prime factorization is of the form 4*m + 3.

The asymptotic density of this sequence is 1 - zeta(4)/zeta(3) = 0.0996073223... (Cohen, 1963).

The number of divisors of all the terms is divisible by 4.

Examples

			8 is a term since 8 = 2^3 and 3 is of the form 4*m + 3.
		

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.

Crossrefs

Complement of A336592.

Complement of A336594 within A252849.

Cf. A002117, A008835, A013662, A036966.

A176297 is a subsequence.

Programs

Mathematica

Select[Range[540], Max[Mod[FactorInteger[#][[;; , 2]], 4]] == 3 &]