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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.

%I A216920 #11 Oct 03 2012 18:02:21
%S A216920 1,2,3,6,10,12,20,30,42,60,120,210,420,630,840,2520,9240,10080,27720,
%T A216920 55440,120120,360360,720720,2162160,6126120,12252240,36756720,
%U A216920 116396280,232792560,698377680,2677114440,5354228880,26771144400,155272637520,465817912560
%N A216920 m such that the integer part of sigma(m)/phi(m) is not attained by any integer less than m.
%C A216920 For large n we expect the inclusion n <= sigma(a(n))/phi(a(n)) <= n+1.
%e A216920 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 A216920_list := proc(searchlimit)
%p A216920 local p, q, P, R; with(numtheory):
%p A216920 P := {}; R := NULL; p := 1;
%p A216920 while p < searchlimit do
%p A216920    q := iquo(sigma(p), phi(p));
%p A216920    if not member(q, P) then
%p A216920       P := {q} union P; R := R,p fi;
%p A216920    p := p+1 od:
%p A216920 R end:
%p A216920 A216920_list(1000);
%o A216920 (Sage)
%o A216920 def A216920_list(searchlimit):
%o A216920     P = {}
%o A216920     for p in (1..searchlimit):
%o A216920         q = sigma(p)//euler_phi(p)
%o A216920         if q not in P: P[q] = p
%o A216920     return sorted(P.values())
%o A216920 A216920_list(1000)
%Y A216920 Cf. A185339.
%K A216920 nonn
%O A216920 1,2
%A A216920 _Peter Luschny_, Sep 30 2012
%E A216920 a(31)-a(33) from _Donovan Johnson_, Oct 02 2012
%E A216920 a(34)-a(35) from _Donovan Johnson_, Oct 03 2012