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A210732
Numbers n for which sigma*(n)=sigma*(x)+sigma*(y), where n=x+y and sigma*(n) is the sum of the anti-divisors of n.
3
6, 9, 15, 18, 21, 24, 27, 30, 31, 33, 37, 39, 43, 44, 46, 47, 53, 56, 57, 62, 65, 66, 70, 73, 74, 75, 76, 78, 81, 83, 86, 88, 90, 91, 92, 93, 97, 99, 102, 103, 106, 107, 109, 110, 114, 116, 117, 118, 119, 121, 122, 123, 125, 126, 127, 129, 131, 133, 135, 136
OFFSET
3,1
COMMENTS
Similar to A211223 but using anti-divisors.
EXAMPLE
sigma*(127)=sigma*(45)+sigma*(82) that is 212=86+126.
In more than one way:
sigma*(133)=sigma*(50)+sigma*(83)=sigma*(52)+sigma*(81) that is
204=80+124=94+110.
MAPLE
with(numtheory);
A210732:=proc(q)
local a, b, c, i, j, k, n;
for n from 3 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;
for i from 1 to trunc(n/2) do
b:=0; c:=0;
for k from 2 to i-1 do if abs((i mod k)-k/2)<1 then b:=b+k; fi; od;
for k from 2 to n-i-1 do if abs(((n-i) mod k)-k/2)<1 then c:=c+k; fi; od;
if a=b+c then print(n); break; fi;
od;
od; end:
A210732(10000);
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 10 2012
STATUS
approved