cp's OEIS Frontend

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.

%I A192291 #12 Sep 28 2015 03:31:54
%S A192291 10,14,32,58,154,182,382,758,3830,5962,67815454,94941602,7172169026,
%T A192291 8196764584,18624907238,34790550682,30033199624,31387575416,
%U A192291 38857270202,48571587730
%N 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.
%C A192291 a(21) > 10^11. - _Hiroaki Yamanouchi_, Sep 28 2015
%e A192291 sigma*(10) = 3+4+7 = 14.
%e A192291 sigma(14)-14 = 1+2+7 = 10.
%e A192291 sigma*(32)= 3+5+7+9+13+21 = 58.
%e A192291 sigma(58)-58 = 1+2+29 = 32.
%p A192291 with(numtheory);
%p A192291 P:= proc(n)
%p A192291 local a,b,c,i,ks;
%p A192291 for i from 3 to n do
%p A192291    a:={};
%p A192291    for k from 2 to i-1 do
%p A192291      if abs((i mod k)- k/2) < 1 then
%p A192291        a:=a union {k};
%p A192291      fi;
%p A192291    od;
%p A192291    b:=nops(a); c:=op(a); s:=0;
%p A192291    for k from 1 to b do
%p A192291        s:=s+c[k];
%p A192291    od;
%p A192291    if sigma(s)-s=i then
%p A192291       print(i,s);
%p A192291    fi;
%p A192291 od;
%p A192291 end:
%p A192291 P(10000);
%Y A192291 Cf. A063990, A066272, A192290, A192292, A192293.
%K A192291 nonn,more
%O A192291 1,1
%A A192291 _Paolo P. Lava_, Jun 29 2011
%E A192291 a(11)-a(20) from _Hiroaki Yamanouchi_, Sep 28 2015