A247022 Integers m such that there is exactly one k < m with sigma(k)/k > sigma(m)/m, sigma(m) being the sum of the divisors of m.

3, 8, 18, 30, 72, 168, 420, 3360, 7560, 12600, 20160, 30240, 32760, 50400, 65520, 83160, 131040, 221760, 831600, 1081080, 1663200, 1801800, 2882880, 6486480, 12252240, 24504480, 41081040, 43243200, 68468400, 82162080, 136936800, 205405200, 245044800, 410810400

Offset

1,1

Comments

Integers such that A247015(n) = 1.

Links

Table of n, a(n) for n=1..34.

Example

sigma(8)/8 is greater than all sigma(x)/x when x < 8 except 6; so 8 is here.

Maple

M1:= 3/2: M2:= 1: c1:= 1:
Res:= NULL: count:= 0:
for n from 3 while count < 20 do
  v:= numtheory:-sigma(n)/n;
  if v > M1 then M2:= M1; M1:= v; c1:= 1
  elif v = M1 then
     c1:= c1+1
  elif c1 = 1 and v >= M2 then
     M2:= v;
     Res:= Res, n: count:= count+1
  fi
od:
Res; # Robert Israel, Jul 28 2020

Prog

(PARI) lista(nn) = {my(t=1, x=3/2, y); for(m=3, nn, if((g=sigma(m)/m)>x, t=1; y=x; x=g, if(g==x, t=0, if(g>=y&&t, y=g; print1(m, ", "))))); } \\ Jinyuan Wang, Jul 28 2020

Crossrefs

Cf. A000203 (sigma), A004394 (superabundant), A017665 and A017666 (sigma(n)/n).

Cf. A247015.

Sequence in context: A288249 A360139 A004210 * A119881 A184636 A075342

Adjacent sequences: A247019 A247020 A247021 * A247023 A247024 A247025

Keyword

nonn

Author

Michel Marcus, Sep 09 2014

Extensions

a(15)-a(21) from Robert Israel, Jun 08 2018

Corrected and name changed by Robert Israel, Jul 28 2020

More terms from Jinyuan Wang, Jul 28 2020

Status

approved