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

Author

Michel Marcus, Sep 09 2014

Keywords

• nonn

Comments

Integers such that A247015(n) = 1.

Examples

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

Crossrefs

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

Cf. A247015.

Programs

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

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

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