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A293708 Numbers n such that phi(sigma(n))/n > phi(sigma(m))/m for all m < n, where sigma is the sum of divisors function (A000203) and phi is Euler's totient function (A000010). 0
1, 4, 16, 36, 144, 576, 3600, 14400, 32400, 129600, 291600, 1166400, 8643600, 34574400, 77792400, 84272400, 311169600, 337089600, 700131600, 2800526400, 179233689600, 202338032400, 809352129600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Makowski and Schinzel proved that lim sup phi(sigma(n))/n = oo, thus this sequence is infinite.

LINKS

Table of n, a(n) for n=1..23.

Andrzej Makowski and Andrzej Schinzel, On the functions phi(n) and sigma(n), Colloquium Mathematicae, Vol. 13, No. 1 (1964), pp. 95-99.

MATHEMATICA

a={}; rm=0; Do[r = EulerPhi[DivisorSigma[1, n]]/n; If[r>rm, rm=r; AppendTo[a, n]], {n, 1, 100000}]; a

PROG

(PARI) lista(nn) = {my(rmax = 0); for (n=1, nn, if ((r=eulerphi(sigma(n))/n) > rmax, rmax = r; print1(n, ", ")); ); } \\ Michel Marcus, Oct 18 2017

CROSSREFS

Cf. A000010, A000203, A062401.

Sequence in context: A176471 A046952 A318278 * A081456 A223403 A263385

Adjacent sequences:  A293705 A293706 A293707 * A293709 A293710 A293711

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Oct 15 2017

EXTENSIONS

a(21)-a(23) from Robert G. Wilson v, Oct 16 2017

STATUS

approved

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Last modified May 16 05:55 EDT 2021. Contains 343939 sequences. (Running on oeis4.)