A192291 Couple of numbers a, b for which sigma*(a)=b and sigma(b)-b=a, where sigma*(n) is the sum of the anti-divisors of n.

10, 14, 32, 58, 154, 182, 382, 758, 3830, 5962, 67815454, 94941602, 7172169026, 8196764584, 18624907238, 34790550682, 30033199624, 31387575416, 38857270202, 48571587730

Offset: 1

Author

Paolo P. Lava, Jun 29 2011

Keywords

• nonn
• more

Comments

a(21) > 10^11. - Hiroaki Yamanouchi, Sep 28 2015

Examples

			sigma*(10) = 3+4+7 = 14.
sigma(14)-14 = 1+2+7 = 10.
sigma*(32)= 3+5+7+9+13+21 = 58.
sigma(58)-58 = 1+2+29 = 32.
		

Crossrefs

Cf. A063990, A066272, A192290, A192292, A192293.

Programs

Maple

with(numtheory);
P:= proc(n)
local a,b,c,i,ks;
for i from 3 to n do
   a:={};
   for k from 2 to i-1 do
     if abs((i mod k)- k/2) < 1 then
       a:=a union {k};
     fi;
   od;
   b:=nops(a); c:=op(a); s:=0;
   for k from 1 to b do
       s:=s+c[k];
   od;
   if sigma(s)-s=i then
      print(i,s);
   fi;
od;
end:
P(10000);

Extensions

a(11)-a(20) from Hiroaki Yamanouchi, Sep 28 2015