A227011 Integers m such that phi(sigma(k))/sigma(phi(k)) > phi(sigma(m))/sigma(phi(m)) for all k

1, 3, 5, 11, 13, 17, 29, 41, 181, 209, 377, 779, 3239, 4469, 5249, 15539, 43259, 58589, 119279, 169679, 174719, 461369, 692687, 955499, 1258949, 1859129, 1917299, 3925463, 7991693, 8986469, 13244069, 16732169, 30629363, 44137523, 48466987, 64018433, 68787773

Offset: 1

Author

Vladimir Letsko, Oct 09 2013

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..48 (terms < 10^10)

Crossrefs

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

Programs

Maple

A062401 := proc(n)
    numtheory[phi](numtheory[sigma](n))
end proc:
A062402 := proc(n)
    numtheory[sigma](numtheory[phi](n))
end proc:
s := proc(n)
    A062401(n)/A062402(n) ;
end proc:
r := 100000000000000000000000000000 ;
for n from 1 do
    if s(n) < r then
        printf("%d,\n",n) ;
        r := s(n) ;
    end if;
end do:

PARI

f(n)=eulerphi(sigma(n=factor(n)))/sigma(eulerphi(n))
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

Extensions

a(33)-a(37) from Donovan Johnson, Oct 11 2013