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A367419 a(n) = sqrt(A367418(n)).

%I A367419 #11 Nov 18 2023 10:55:50
%S A367419 1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2,1,3,1,1,1,4,1,1,1,1,1,1,2,1,1,1,
%T A367419 1,1,1,1,3,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,
%U A367419 4,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1
%N A367419 a(n) = sqrt(A367418(n)).
%H A367419 Amiram Eldar, <a href="/A367419/b367419.txt">Table of n, a(n) for n = 1..10000</a>
%H A367419 Michael De Vlieger, <a href="/A367419/a367419.png">Plot f(a(n)) at (x,y) = (n mod m, floor(n/m))</a> for m = 857 and n = 734449, where f is a color function such that 1 = gray, red indicates primes, gold composite prime powers, green squarefree composites, blue and purple numbers neither squarefree nor prime powers, but purple additionally represents squareful numbers that are not prime powers.
%F A367419 a(n) = sqrt(A003557(A268335(n))) = sqrt(A268335(n)/A367417(n)).
%F A367419 a(n) = A268335(n)/A367407(n).
%F A367419 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/A065463 = 1.41956288050548591931... . - _Amiram Eldar_, Nov 17 2023
%t A367419 s[n_] := Sqrt[n / Times @@ FactorInteger[n][[;; , 1]]]; s /@ Select[Range[200], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]
%o A367419 (PARI) b(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2]%2, f[i, 1]^(f[i, 2]-1), 0)); }
%o A367419 lista(kmax) = {my(b1); for(k = 1, kmax, b1 = b(k); if(b1 > 0, print1(sqrtint(b1), ", "))); }
%Y A367419 Cf. A003557, A065463, A268335, A367407, A367417, A367418.
%K A367419 nonn,easy
%O A367419 1,7
%A A367419 _Amiram Eldar_, Nov 17 2023