OFFSET
1,2
COMMENTS
The squarefree numbers (A005117) are terms of this sequence since if k is squarefree, then the largest square dividing k is 1 which is a unitary divisor, sqrt(1) has 0 prime divisors, and 0 is even.
The asymptotic density of this sequence is (5 * Product_{p prime} (1 - 1/(p^2*(p+1))) + 2 * Product_{p prime} (1 + 1/(p^2*(p+1))))/10 = (5 * 0.881513... + 2 * 1.125606...)/10 = 0.665878294481337275662425136416469977597382409701642... (Cohen, 1964; the first product is A065465).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eckford Cohen, Some asymptotic formulas in the theory of numbers, Trans. Amer. Math. Soc., Vol. 112 (1964), pp. 214-227.
EXAMPLE
16 is a term since the largest square dividing 16 is 16, which is a unitary divisor, sqrt(16) = 4, 4 = 2 * 2 has 2 prime divisors, and 2 is even.
MATHEMATICA
seqQ[n_] := AllTrue[(e = FactorInteger[n][[;; , 2]]), # == 1 || EvenQ[#] &] && EvenQ @ Total[Select[e, # > 1 &]/2]; Select[Range[100], seqQ]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 12 2020
STATUS
approved