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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

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

EXAMPLE

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.

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:

PROG

(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

CROSSREFS

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

Sequence in context: A154500 A020578 A250481 * A243627 A178604 A153443

Adjacent sequences:  A227008 A227009 A227010 * A227012 A227013 A227014

KEYWORD

nonn

AUTHOR

Vladimir Letsko, Oct 09 2013

EXTENSIONS

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

STATUS

approved

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Last modified April 23 13:25 EDT 2019. Contains 322386 sequences. (Running on oeis4.)