OFFSET
1,2
COMMENTS
Supersequence of A051676 (composite numbers whose square has a prime number of divisors).
Subsequence of A001694 (powerful numbers).
Numbers whose prime factorization has only exponents that are congruent to {0, 2} mod 3 (A007494). - Amiram Eldar, Mar 31 2022
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = {m : gcd(d(m^2), 6) = 1}.
Sum_{n>=1} 1/a(n) = 15*zeta(3)/Pi^2 (= 10 * A240976). - Amiram Eldar, Mar 31 2022
MAPLE
A350014 := proc(n)
option remember ;
local a;
if n =1 then
1;
else
for a from procname(n-1)+1 do
if igcd(numtheory[tau](a^2), 6) = 1 then
return a;
end if;
end do:
end if;
end proc:
seq(A350014(n), n=1..20) ; # R. J. Mathar, Apr 06 2022
MATHEMATICA
Select[Range[1500], CoprimeQ[DivisorSigma[0, #^2], 6] &] (* or *)
With[{nn = 1500}, Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], Mod[DivisorSigma[0, #^2], 3] != 0 &]]
PROG
(PARI) isok(m) = gcd(numdiv(m^2), 6) == 1; \\ Michel Marcus, Mar 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Jan 17 2022
STATUS
approved