

A192292


Pairs of numbers a, b for which sigma*(a)=b and sigma(b)b1=a, where sigma*(n) is the sum of the antidivisors of n.


3



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

1,1


COMMENTS

Betrothed numbers mixed with antidivisors.
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)861 = 2+43 = 45.
sigma*(2379) = 2+6+26+67+71+78+122+366+1586 = 2374.
sigma(2324)23241 = 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*i1)+sigma(i/2^k)*2^(k+1)6*i2;
if sigma(b)b1=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



