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

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)