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

1,2

Comments

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

Links

Table of n, a(n) for n=1..35.

Example

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.

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);

Prog

(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)

Crossrefs

Cf. A185339.

Sequence in context: A065029 A239212 A280558 * A120754 A023547 A190690

Adjacent sequences: A216917 A216918 A216919 * A216921 A216922 A216923

Keyword

nonn

Author

Peter Luschny, Sep 30 2012

Extensions

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

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

Status

approved