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A227011 Integers n such that phi(sigma(k))/sigma(phi(k)) >  phi(sigma(n))/sigma(phi(n)) for all k<n. 4

%I

%S 1,3,5,11,13,17,29,41,181,209,377,779,3239,4469,5249,15539,43259,

%T 58589,119279,169679,174719,461369,692687,955499,1258949,1859129,

%U 1917299,3925463,7991693,8986469,13244069,16732169,30629363,44137523,48466987,64018433,68787773

%N Integers n such that phi(sigma(k))/sigma(phi(k)) > phi(sigma(n))/sigma(phi(n)) for all k<n.

%C These are the indices where the rational function A062401(n)/A062402(n) drops below the minimum set by all earlier ratios.

%C a(2) to a(9) are primes. However all known terms beginning from a(10) are composite.

%H Donovan Johnson, <a href="/A227011/b227011.txt">Table of n, a(n) for n = 1..48</a> (terms < 10^10)

%e 5 is in the sequence because phi(sigma(5))/sigma(phi(5)) = 2/7 and for all k < 5, phi(sigma(k))/sigma(phi(k)) > 2/7.

%p A062401 := proc(n)

%p numtheory[phi](numtheory[sigma](n))

%p end proc:

%p A062402 := proc(n)

%p numtheory[sigma](numtheory[phi](n))

%p end proc:

%p s := proc(n)

%p A062401(n)/A062402(n) ;

%p end proc:

%p r := 100000000000000000000000000000 ;

%p for n from 1 do

%p if s(n) < r then

%p printf("%d,\n",n) ;

%p r := s(n) ;

%p end if;

%p end do:

%o (PARI) f(n)=eulerphi(sigma(n=factor(n)))/sigma(eulerphi(n))

%o is(n)=my(t=f(n)); for(k=1,n-1,if(f(k)<=t, return(0))); 1 \\ _Charles R Greathouse IV_, Nov 27 2013

%Y Cf. A227927, A062401, A062402, A033632, A229238.

%K nonn

%O 1,2

%A _Vladimir Letsko_, Oct 09 2013

%E a(33)-a(37) from _Donovan Johnson_, Oct 11 2013

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)