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A216213
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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.
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1
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1, 2, 11, 12, 15, 16, 22, 31, 76, 152, 309, 1576, 375479, 781314, 1114986, 3734218, 24311881, 68133239, 147881549
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OFFSET
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1,2
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COMMENTS
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Tested up to k = 108122.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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