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 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. 3
 7, 10, 14, 16, 45, 86, 2379, 2324, 4213, 5866, 27323, 33604, 1303227, 1737628, 3722831, 4208308, 15752651, 18706108, 6094085371, 8114352508, 30090695519, 40119052564 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Betrothed numbers mixed with anti-divisors. a(23) > 10^11. - Hiroaki Yamanouchi, Sep 28 2015 LINKS 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

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)