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A307004 Numbers k such that phi^e(k) > phi^e(m) for all m < k, where phi^e(k) = A072911(k) is the number of divisors d of k such that d and k are exponentially coprime.

%I A307004 #18 May 30 2025 03:50:22
%S A307004 1,8,32,128,864,2048,3456,7776,31104,279936,497664,1990656,4478976,
%T A307004 17915904,62208000,97200000,362797056,559872000,874800000,1555200000,
%U A307004 6220800000,13996800000,55987200000,349920000000,895795200000,1133740800000,1399680000000,4534963200000
%N A307004 Numbers k such that phi^e(k) > phi^e(m) for all m < k, where phi^e(k) = A072911(k) is the number of divisors d of k such that d and k are exponentially coprime.
%C A307004 The corresponding record values of phi^e are 1, 2, 4, 6, 8, 10, 12, 16, 24, ... (see the link for more values).
%D A307004 József Sándor, On an exponential totient function, Studia Univ. Babees-Bolyai, Math., Vol. 41 (1996), pp. 91-94.
%H A307004 Amiram Eldar, <a href="/A307004/b307004.txt">Table of n, a(n) for n = 1..57</a>
%H A307004 Amiram Eldar, <a href="/A307004/a307004.txt">Table of n, a(n), A072911(a(n)) for n = 1..57</a>
%H A307004 László Tóth, <a href="https://ac.inf.elte.hu/Vol_024_2004/doi/285_24.pdf">On certain arithmetic functions involving exponential divisors</a>, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 27 (2004), pp. 285-294.
%t A307004 f[n_] := Times@@EulerPhi[FactorInteger[n][[All,2]]]; fm=0; s={}; Do[f1=f[n]; If[f1>fm, AppendTo[s,n]; fm=f1], {n,1,10^6}]; s
%Y A307004 Cf. A025487, A072911.
%K A307004 nonn
%O A307004 1,2
%A A307004 _Amiram Eldar_, Mar 19 2019