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.

1, 8, 32, 128, 864, 2048, 3456, 7776, 31104, 279936, 497664, 1990656, 4478976, 17915904, 62208000, 97200000, 362797056, 559872000, 874800000, 1555200000, 6220800000, 13996800000, 55987200000, 349920000000, 895795200000, 1133740800000, 1399680000000, 4534963200000

Offset: 1

Author

Amiram Eldar, Mar 19 2019

Keywords

• nonn

Comments

The corresponding record values of phi^e are 1, 2, 4, 6, 8, 10, 12, 16, 24, ... (see the link for more values).

References

• József Sándor, On an exponential totient function, Studia Univ. Babees-Bolyai, Math., Vol. 41 (1996), pp. 91-94.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..57
• Amiram Eldar, Table of n, a(n), A072911(a(n)) for n = 1..57
• László Tóth, On certain arithmetic functions involving exponential divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 27 (2004), pp. 285-294.

Crossrefs

Cf. A025487, A072911.

Programs

Mathematica

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