A216213 Numbers k such that sigma*(k) = Sum_{j=anti-divisors of k} sigma*(j), where sigma*(k) is the sum of the anti-divisors of k.

1, 2, 11, 12, 15, 16, 22, 31, 76, 152, 309, 1576, 375479, 781314, 1114986, 3734218, 24311881, 68133239, 147881549

Offset: 1

Author

Paolo P. Lava, Mar 13 2013

Keywords

• nonn

Comments

Tested up to k = 108122.

a(20) > 3*10^8. - Donovan Johnson, Mar 22 2013

Examples

			Anti-divisors of 76 are 3, 8, 9, 17 and 51 and their sum is 88.
Anti-divisor of 3 is 2 -> Sum is 2.
Anti-divisors of 8 are 3 and 5 -> Sum is 8.
Anti-divisors of 9 are 2 and 6 -> Sum is 8.
Anti-divisors of 17 are 2, 3, 5, 7 and 11 -> Sum is 28.
Anti-divisors of 51 are 2, 6 and 34 -> Sum is 42.
Finally, 2+8+8+28+42=88.
		

Crossrefs

Cf. A066272, A178029, A191580, A191581, A192282-A192284.

Programs

Maple

A216213:= proc(q) local a,b,c,j,k,n;
for n from 1 to q do
  a:={}; b:=0; for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then b:=b+k; a:=a union {k}; fi; od;
  c:=0; for j from 1 to nops(a) do for k from 2 to a[j]-1 do if abs((a[j] mod k)-k/2)<1 then c:=c+k; fi; od; od; if b=c then print(n); fi; od; end:
A216213(10^10);

Extensions

a(13)-a(19) from Donovan Johnson, Mar 22 2013