OFFSET
1,2
COMMENTS
First differs from A197680 at n = 331, from A274034 at n = 42, from A361177 at n = 167, and from A366762 at n = 84.
Equivalently, square roots of the numbers whose number of divisors is a power of 3.
The asymptotic density of this sequence is Product_{p prime} ((1 - 1/p) * Sum_{k>=0} 1/p^((3^k-1)/2)) = 0.64033435998103973346... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n)^2 = Product_{p prime} Sum_{k>=0} 1/p^(3^k-1) = 1.52478035628964060288... .
MATHEMATICA
pow3q[n_] := n == 3^IntegerExponent[n, 3]; Select[Range[100], pow3q[DivisorSigma[0, #^2]] &]
PROG
(PARI) ispow3(n) = n == 3^valuation(n, 3);
is(n) = ispow3(numdiv(n^2));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 16 2024
STATUS
approved