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%I #7 Oct 28 2023 03:48:35
%S 1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,8,1,1,27,1,1,1,1,32,1,
%T 1,1,1,1,1,1,8,1,1,1,1,1,1,1,8,1,1,1,1,1,27,1,8,1,1,1,1,1,1,1,64,1,1,
%U 1,1,1,1,1,8,1,1,1,1,1,1,1,8,27,1,1,1,1,1
%N The largest exponentially evil divisor of n.
%C The largest divisor of n that is an exponentially evil number (A262675).
%C The number of exponentially evil divisors of n is A366902(n) and their sum is A366904(n).
%H Amiram Eldar, <a href="/A366906/b366906.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p^max{k=1..e, k evil}.
%F a(n) <= n, with equality if and only if n is exponentially evil number (A262675).
%F a(n) >= 1, with equality if and only if n is a cubefree number (A004709).
%t maxEvil[e_] := Module[{k = e}, While[OddQ[DigitCount[k, 2, 1]], k--]; k]; f[p_, e_] := p^maxEvil[e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) s(n) = {my(k = n); while(hammingweight(k)%2, k--); k;}
%o a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2]));}
%Y Cf. A004709, A262675, A366902, A366904.
%Y Similar sequences: A353897, A365683, A366905.
%K nonn,easy,mult
%O 1,8
%A _Amiram Eldar_, Oct 27 2023