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

1,1

Comments

Betrothed numbers mixed with anti-divisors.

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

Links

Table of n, a(n) for n=1..22.

Example

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.

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);

Crossrefs

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

Sequence in context: A080205 A108980 A005526 * A030123 A191833 A020752

Adjacent sequences: A192289 A192290 A192291 * A192293 A192294 A192295

Keyword

nonn,more,tabf

Author

Paolo P. Lava, Jun 29 2011

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

Status

approved