A192292 Pairs of numbers a, b for which sigma*(a)=b and sigma(b)-b-1=a, where sigma*(n) is the sum of the anti-divisors of n.

7, 10, 14, 16, 45, 86, 2379, 2324, 4213, 5866, 27323, 33604, 1303227, 1737628, 3722831, 4208308, 15752651, 18706108, 6094085371, 8114352508, 30090695519, 40119052564

Offset: 1

Author

Paolo P. Lava, Jun 29 2011

Keywords

• nonn
• more
• tabf

Comments

Betrothed numbers mixed with anti-divisors.

a(23) > 10^11. - Hiroaki Yamanouchi, Sep 28 2015

Examples

			sigma*(45)= 2+6+7+10+13+18+30 = 86.
sigma(86)-86-1 = 2+43 = 45.
sigma*(2379) = 2+6+26+67+71+78+122+366+1586 = 2374.
sigma(2324)-2324-1 = 2+4+7+14+28+83+166+332+581+1162 = 2379.
		

Crossrefs

Cf. A005276, A066272, A192290, A192291, A192293.

Programs

Maple

with(numtheory); P:= proc(n) local b,c,i,j,k;
for i from 3 to n do k:=0; j:=i;
while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
b:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2;
if sigma(b)-b-1=i then print(i); print(b); fi;
od; end: P(10^9);

Extensions

a(13)-a(14) from Paolo P. Lava, Dec 03 2014

a(7)-a(8) swapped and a(15)-a(22) added by Hiroaki Yamanouchi, Sep 28 2015