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A303218
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A(n,k) is the n-th Fibonacci number with exactly k distinct prime factors; square array A(n,k), n>=1, k>=1, read by antidiagonals.
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5
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2, 21, 3, 610, 34, 5, 6765, 987, 55, 8, 832040, 46368, 2584, 144, 13, 102334155, 14930352, 196418, 10946, 377, 89, 190392490709135, 4807526976, 267914296, 317811, 3524578, 4181, 233, 1548008755920, 37889062373143906, 86267571272, 701408733, 2178309, 9227465, 17711, 1597
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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Square array A(n,k) begins:
2, 21, 610, 6765, 832040, 102334155, ...
3, 34, 987, 46368, 14930352, 4807526976, ...
5, 55, 2584, 196418, 267914296, 86267571272, ...
8, 144, 10946, 317811, 701408733, 225851433717, ...
13, 377, 3524578, 2178309, 1134903170, 10610209857723, ...
89, 4181, 9227465, 32951280099, 12586269025, 8944394323791464, ...
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MAPLE
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F:= combinat[fibonacci]: with(numtheory):
A:= proc() local h, p, q; p, q:= proc() [] end, 2;
proc(n, k)
while nops(p(k))<n do q:= q+1;
h:= nops(factorset(F(q)));
p(h):= [p(h)[], F(q)]
od; p(k)[n]
end
end():
seq(seq(A(n, 1+d-n), n=1..d), d=1..12);
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MATHEMATICA
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nmax = 12(*rows*);
maxIndex = 200; (* increase if message "part does not exist" *)
nu[n_] := nu[n] = PrimeNu[Fibonacci[n]];
col[k_] := Select[Range[maxIndex], nu[#] == k &];
T = Array[col, nmax];
A[n_, k_] := Fibonacci[T[[k, n]]];
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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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