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A219053
Numbers which are the sum of their proper divisors and their anti-divisors.
1
3, 19, 131, 139, 649, 3649, 4181, 5881, 13369, 29501, 65789, 37548761, 63919409, 2471800109
OFFSET
1,1
COMMENTS
a(15) > 10^10. - Donovan Johnson, Apr 19 2013
EXAMPLE
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.
MAPLE
with(numtheory); A219053:=proc(q) local a, k, n;
for n from 1 to q do a:=0;
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;
if 2*n=sigma(n)+a then print(n); fi; od; end: A219053(10^6);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Apr 17 2013
EXTENSIONS
a(12)-a(14) from Donovan Johnson, Apr 19 2013
STATUS
approved