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

1, 2, 3, 6, 10, 12, 20, 30, 42, 60, 120, 210, 420, 630, 840, 2520, 9240, 10080, 27720, 55440, 120120, 360360, 720720, 2162160, 6126120, 12252240, 36756720, 116396280, 232792560, 698377680, 2677114440, 5354228880, 26771144400, 155272637520, 465817912560

Offset: 1

Author

Peter Luschny, Sep 30 2012

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A185339.

Programs

Maple

A216920_list := proc(searchlimit)
local p, q, P, R; with(numtheory):
P := {}; R := NULL; p := 1;
while p < searchlimit do
   q := iquo(sigma(p), phi(p));
   if not member(q, P) then
      P := {q} union P; R := R,p fi;
   p := p+1 od:
R end:
A216920_list(1000);

Sage

def A216920_list(searchlimit):
    P = {}
    for p in (1..searchlimit):
        q = sigma(p)//euler_phi(p)
        if q not in P: P[q] = p
    return sorted(P.values())
A216920_list(1000)

Extensions

a(31)-a(33) from Donovan Johnson, Oct 02 2012

a(34)-a(35) from Donovan Johnson, Oct 03 2012