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A293234 a(n) is the number of proper divisors of n that are square.

%I A293234 #17 Dec 01 2023 15:53:35
%S A293234 0,1,1,1,1,1,1,2,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,1,2,2,1,1,1,3,1,1,
%T A293234 1,3,1,1,1,2,1,1,1,2,2,1,1,3,1,2,1,2,1,2,1,2,1,1,1,2,1,1,2,3,1,1,1,2,
%U A293234 1,1,1,4,1,1,2,2,1,1,1,3,2,1,1,2,1,1,1,2,1,2,1,2,1,1,1,3,1,2,2,3,1,1,1,2,1
%N A293234 a(n) is the number of proper divisors of n that are square.
%C A293234 First occurrence of k: 2, 8, 32, 72, 144, 288, 576, 1152, 2304, 4608, 3600, 7200, 36864, 20736, 14400, 28800, 32400, 64800, 57600, 115200, 663552, 18874368, 129600, 259200, 3359232, 810000, 921600, 1843200, 518400, 1036800, 705600, 1411200, etc. - _Robert G. Wilson v_, Oct 08 2017
%H A293234 Antti Karttunen, <a href="/A293234/b293234.txt">Table of n, a(n) for n = 1..16384</a>
%H A293234 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A293234 a(n) = Sum_{d|n, d<n} A010052(d).
%F A293234 a(n) = A046951(n) - A010052(n).
%F A293234 G.f.: Sum_{k>=1} x^(2*k^2) / (1 - x^(k^2)). - _Ilya Gutkovskiy_, Apr 13 2021
%F A293234 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi^2/6 (A013661). - _Amiram Eldar_, Dec 01 2023
%t A293234 f[n_] := Length@ Select[ Sqrt@ Most@ Divisors@ n, IntegerQ]; Array[f, 105] (* _Robert G. Wilson v_, Oct 08 2017 *)
%o A293234 (PARI) A293234(n) = sumdiv(n,d,(d<n)*ispower(d,2));
%Y A293234 Cf. A010052, A013661, A046951, A293227, A293235.
%K A293234 nonn
%O A293234 1,8
%A A293234 _Antti Karttunen_, Oct 08 2017