cp's OEIS Frontend

A369210 Numbers k such that the number of divisors of k^2 is a power of 3.

%I A369210 #8 Jan 16 2024 06:58:10
%S A369210 1,2,3,5,6,7,10,11,13,14,15,16,17,19,21,22,23,26,29,30,31,33,34,35,37,
%T A369210 38,39,41,42,43,46,47,48,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,
%U A369210 74,77,78,79,80,81,82,83,85,86,87,89,91,93,94,95,97,101,102
%N A369210 Numbers k such that the number of divisors of k^2 is a power of 3.
%C A369210 First differs from A197680 at n = 331, from A274034 at n = 42, from A361177 at n = 167, and from A366762 at n = 84.
%C A369210 Equivalently, square roots of the numbers whose number of divisors is a power of 3.
%C A369210 The asymptotic density of this sequence is Product_{p prime} ((1 - 1/p) * Sum_{k>=0} 1/p^((3^k-1)/2)) = 0.64033435998103973346... .
%H A369210 Amiram Eldar, <a href="/A369210/b369210.txt">Table of n, a(n) for n = 1..10000</a>
%F A369210 Sum_{n>=1} 1/a(n)^2 = Product_{p prime} Sum_{k>=0} 1/p^(3^k-1) = 1.52478035628964060288... .
%t A369210 pow3q[n_] := n == 3^IntegerExponent[n, 3]; Select[Range[100], pow3q[DivisorSigma[0, #^2]] &]
%o A369210 (PARI) ispow3(n) = n == 3^valuation(n, 3);
%o A369210 is(n) = ispow3(numdiv(n^2));
%Y A369210 Cf. A000005, A000244, A000290.
%Y A369210 Cf. A197680, A274034, A361177, A366762.
%K A369210 nonn,easy
%O A369210 1,2
%A A369210 _Amiram Eldar_, Jan 16 2024