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

1,1

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.

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

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

Mathematica

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

Crossrefs

Complement of A336592.

Complement of A336594 within A252849.

Cf. A002117, A008835, A013662, A036966.

A176297 is a subsequence.

Sequence in context: A374459 A195086 A366761 * A176297 A375072 A175496

Adjacent sequences: A336590 A336591 A336592 * A336594 A336595 A336596

Keyword

nonn

Author

Amiram Eldar, Jul 26 2020

Status

approved