A219053 Numbers which are the sum of their proper divisors and their anti-divisors.

3, 19, 131, 139, 649, 3649, 4181, 5881, 13369, 29501, 65789, 37548761, 63919409, 2471800109

Offset: 1

Author

Paolo P. Lava, Apr 17 2013

Keywords

• nonn
• more

Comments

a(15) > 10^10. - Donovan Johnson, Apr 19 2013

Examples

			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.
		

Crossrefs

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

Programs

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);

Extensions

a(12)-a(14) from Donovan Johnson, Apr 19 2013