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A216920 m such that the integer part of sigma(m)/phi(m) is not attained by any integer less than m. 0

%I

%S 1,2,3,6,10,12,20,30,42,60,120,210,420,630,840,2520,9240,10080,27720,

%T 55440,120120,360360,720720,2162160,6126120,12252240,36756720,

%U 116396280,232792560,698377680,2677114440,5354228880,26771144400,155272637520,465817912560

%N m such that the integer part of sigma(m)/phi(m) is not attained by any integer less than m.

%C For large n we expect the inclusion n <= sigma(a(n))/phi(a(n)) <= n+1.

%e a(22) = 360360 is in this list because sigma(360360)/phi(360360) = 22.75 and floor(sigma(k)/phi(k)) != 22 for all k < 360360.

%p A216920_list := proc(searchlimit)

%p local p, q, P, R; with(numtheory):

%p P := {}; R := NULL; p := 1;

%p while p < searchlimit do

%p q := iquo(sigma(p), phi(p));

%p if not member(q, P) then

%p P := {q} union P; R := R,p fi;

%p p := p+1 od:

%p R end:

%p A216920_list(1000);

%o (Sage)

%o def A216920_list(searchlimit):

%o P = {}

%o for p in (1..searchlimit):

%o q = sigma(p)//euler_phi(p)

%o if q not in P: P[q] = p

%o return sorted(P.values())

%o A216920_list(1000)

%Y Cf. A185339.

%K nonn

%O 1,2

%A _Peter Luschny_, Sep 30 2012

%E a(31)-a(33) from _Donovan Johnson_, Oct 02 2012

%E a(34)-a(35) from _Donovan Johnson_, Oct 03 2012

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Last modified August 4 11:27 EDT 2021. Contains 346447 sequences. (Running on oeis4.)