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Numbers which are the sum of their proper divisors and their anti-divisors.
1

%I #17 Apr 22 2013 03:03:08

%S 3,19,131,139,649,3649,4181,5881,13369,29501,65789,37548761,63919409,

%T 2471800109

%N Numbers which are the sum of their proper divisors and their anti-divisors.

%C a(15) > 10^10. - _Donovan Johnson_, Apr 19 2013

%e The proper divisors of 649 are 1, 11, 59 and its anti-divisors are 2, 3, 22, 118, 433. Their sum 1+11+59+2+3+22+118+433 is equal to 649.

%p with(numtheory); A219053:=proc(q) local a,k,n;

%p for n from 1 to q do a:=0;

%p for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;

%p if 2*n=sigma(n)+a then print(n); fi; od; end: A219053(10^6);

%Y Cf. A000005, A000396, A001065, A066272, A066417, A073930.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Apr 17 2013

%E a(12)-a(14) from _Donovan Johnson_, Apr 19 2013