OFFSET
1,2
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...
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
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.
MATHEMATICA
Select[Range[100], Max[Mod[FactorInteger[#][[;; , 2]], 4]] < 3 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 26 2020
STATUS
approved