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A068333
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Product(n/k - k) where the product is over the divisors k of n and where 1 <= k <= sqrt(n).
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2
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0, 1, 2, 0, 4, 5, 6, 14, 0, 27, 10, 44, 12, 65, 28, 0, 16, 357, 18, 152, 80, 189, 22, 2300, 0, 275, 156, 972, 28, 2639, 30, 1736, 256, 495, 68, 0, 36, 629, 380, 12636, 40, 8569, 42, 6020, 2112, 945, 46, 215072, 0, 5635, 700, 11016, 52, 59625
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OFFSET
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1,3
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COMMENTS
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a(n) is divisible by n-1.
a(n) = 0 if and only if n is a square.
a(n) = n-1 if n is prime. (End)
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LINKS
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EXAMPLE
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a(8) = (8 - 1) (4 - 2) = 14 because 1 and 2 are the divisors of 8 which are <= sqrt(8).
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MAPLE
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f:= proc(n) local D, k;
D:= select(t -> t^2 <= n, numtheory:-divisors(n));
mul(n/k-k, k=D)
end proc:
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MATHEMATICA
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a[n_] := Product[If[1 <= k <= Sqrt[n], (n/k - k), 1], {k, Divisors[n]}];
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PROG
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(PARI) a(n) = my(p=1); fordiv(n, d, if (d^2 <= n, p *= n/d - d)); p; \\ Michel Marcus, Jun 02 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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