A336592 Numbers k such that k/A008835(k) is cubefree, where A008835(k) is the largest 4th power dividing k.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75

Offset: 1

Author

Amiram Eldar, Jul 26 2020

Keywords

• nonn

Comments

Numbers such that none of the exponents in their prime factorization is of the form 4*m + 3.

Cohen (1963) proved that for a given number k > 2 the asymptotic density of numbers whose exponents in their prime factorization are not of the forms k*m - 1 is zeta(k)/zeta(k-1). In this sequence k = 4, and therefore its asymptotic density is zeta(4)/zeta(3) = Pi^4/(90*zeta(3)) = 0.9003926776...

Examples

			6 is a term since 6 = 2^1 * 3^1 and 1 is not of the form 4*m + 3.
8 is not 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

Cf. A002117, A004709, A008835, A013662.

Programs

Mathematica

Select[Range[100], Max[Mod[FactorInteger[#][[;; , 2]], 4]] < 3 &]