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A259124
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If n is representable as x*y+x+y, with x>=y>1, then a(n) is the sum of all x's and y's in all such representations. Otherwise a(n)=0.
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4
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0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 6, 6, 0, 7, 0, 7, 8, 0, 0, 17, 8, 0, 10, 9, 0, 20, 0, 10, 12, 0, 10, 34, 0, 0, 14, 23, 0, 26, 0, 13, 28, 0, 0, 43, 12, 13, 18, 15, 0, 32, 14, 29, 20, 0, 0, 67, 0, 0, 36, 32, 16, 38, 0, 19, 24, 32, 0, 76, 0, 0, 44, 21, 16, 44, 0, 57, 44
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OFFSET
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1,8
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COMMENTS
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The sequence of numbers that never appear in a(n) begins: 1, 2, 3, 11, 27, 35, 51, 53, 79, 83, 89, 93, 117, 123, 125, 135, 143, 145.
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LINKS
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FORMULA
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a(n) = Sum({d: d | n+1 and 3 <= d <= sqrt(n+1)}, d + (n+1)/d - 2). - Robert Israel, Aug 05 2015
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EXAMPLE
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11 = 3*2 + 3 + 2, so a(11)=5.
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MAPLE
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f:= proc(n) local D, d;
D:= select(t -> (t >= 3 and t^2 <= n+1), numtheory:-divisors(n+1));
add(d + (n+1)/d - 2, d = D);
end proc:
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MATHEMATICA
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a[n_] := Sum[Boole[3 <= d <= Sqrt[n+1]] (d+(n+1)/d-2), {d, Divisors[n+1]}];
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PROG
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(Python)
TOP = 100
a = [0]*TOP
for y in range(2, TOP//2):
for x in range(y, TOP//2):
n = x*y + x + y
if n>=TOP: break
a[n] += x+y
print(a[1:])
(PARI) a(n)=sum(y=2, sqrtint(n+1)-1, my(x=(n-y)/(y+1)); if(denominator(x)==1, x+y)) \\ Charles R Greathouse IV, Jun 29 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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