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A368167 The largest unitary divisor of n that is a cubefull exponentially odd number (A335988).

%I A368167 #10 Dec 16 2023 09:01:39
%S A368167 1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,1,1,27,1,1,1,1,32,1,
%T A368167 1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,27,1,8,1,1,1,1,1,1,1,1,1,1,1,
%U A368167 1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A368167 The largest unitary divisor of n that is a cubefull exponentially odd number (A335988).
%C A368167 First differs from A056191 and A366126 at n = 32, and from A367513 at n = 64.
%C A368167 Also, the largest exponentially odd unitary divisor of the powerful part on n.
%C A368167 Also, the powerful part of the largest exponentially odd unitary divisor of n.
%H A368167 Amiram Eldar, <a href="/A368167/b368167.txt">Table of n, a(n) for n = 1..10000</a>
%F A368167 Multiplicative with a(p^e) = p^e if e is odd that is larger than 1, and 1 otherwise.
%F A368167 a(n) = A350389(A057521(n)).
%F A368167 a(n) = A057521(A350389(n)).
%F A368167 a(n) >= 1, with equality if and only if n is in A335275.
%F A368167 a(n) <= n, with equality if and only if n is in A335988.
%t A368167 f[p_, e_] := If[e == 1 || EvenQ[e], 1, p^e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A368167 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1 || !(f[i, 2]%2), 1, f[i, 1]^f[i, 2]));}
%Y A368167 Cf. A057521, A077610, A335275, A335988, A350389, A368168, A368169.
%Y A368167 Cf. A056191, A366126, A367513.
%K A368167 nonn,easy,mult
%O A368167 1,8
%A A368167 _Amiram Eldar_, Dec 14 2023