%N Numbers n for which the number of divisors, tau(n), is divisible by 3.
%C tau(n) is divisible by 3 iff at least one prime in the prime factorization of n has exponent of the form 3*m + 2. This sequence is an extension of the sequence A038109 in which the numbers has at least one prime with exponent 2 (the case of m = 0 here ) in their prime factorization.
%C The union of A211337 and A211338 is the complementary sequence to this one. [_Douglas Latimer_, Apr 12 2012]
%H Charles R Greathouse IV, <a href="/A059269/b059269.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjecture: a(n) ~ k*n where k = 1/(1 - prod(1 - (p-1)/(p^(3*k)))) = 3.743455... where p ranges over the primes and k ranges over the positive integers. - _Charles R Greathouse IV_, Apr 13 2012
%e a(7) = 28 because the number of divisors of 28 d(28) = 6
%p with(numtheory): for n from 1 to 1000 do if tau(n) mod 3 = 0 then printf(`%d,`,n) fi: od:
%o (PARI) is(n)=vecmax(factor(n)[,2]%3)==2 \\ _Charles R Greathouse IV_, Apr 10 2012
%o (PARI) is(n)=numdiv(n)%3==0 \\ _Charles R Greathouse IV_, Sep 18 2015
%Y Cf. A038109, A000005, A211337, A211338.
%A Avi Peretz (njk(AT)netvision.net.il), Jan 24 2001
%E More terms from _James A. Sellers_, Jan 24 2001