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A367418 The exponentially odd numbers (A268335) divided by their squarefree kernels (A007947).

%I A367418 #14 Nov 30 2023 02:53:03
%S A367418 1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,4,1,9,1,1,1,16,1,1,1,1,1,1,4,1,1,1,
%T A367418 1,1,1,1,9,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,
%U A367418 16,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,4,1
%N A367418 The exponentially odd numbers (A268335) divided by their squarefree kernels (A007947).
%C A367418 Analogous to A102631, with the exponentially odd numbers instead of the square numbers (A000290).
%C A367418 All the terms are square numbers.
%H A367418 Amiram Eldar, <a href="/A367418/b367418.txt">Table of n, a(n) for n = 1..10000</a>
%F A367418 a(n) = A003557(A268335(n)).
%F A367418 a(n) = A268335(n)/A367417(n).
%F A367418 a(n) = A367419(n)^2.
%F A367418 a(n) = A268335(n)^2/A367406(n).
%F A367418 a(n) = A008833(A268335(n)). - _Amiram Eldar_, Nov 30 2023
%t A367418 s[n_] := n / Times @@ FactorInteger[n][[;; , 1]]; s /@ Select[Range[200], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]
%o A367418 (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 A367418 lista(kmax) = {my(b1); for(k = 1, kmax, b1 = b(k); if(b1 > 0, print1(b1, ", "))); }
%Y A367418 Cf. A000290, A008833, A102631, A268335, A367406, A367417, A367419.
%K A367418 nonn,easy
%O A367418 1,7
%A A367418 _Amiram Eldar_, Nov 17 2023