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A303216
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A(n,k) is the n-th Fibonacci number with exactly k prime factors (counted with multiplicity); square array A(n,k), n>=1, k>=1, read by antidiagonals.
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6
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2, 21, 3, 8, 34, 5, 6765, 610, 55, 13, 2584, 196418, 987, 377, 89, 144, 701408733, 317811, 10946, 4181, 233, 832040, 102334155, 1134903170, 2178309, 75025, 17711, 1597, 86267571272, 267914296, 12586269025, 365435296162, 32951280099, 3524578, 121393, 28657
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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, 8, 6765, 2584, 144, ...
3, 34, 610, 196418, 701408733, 102334155, ...
5, 55, 987, 317811, 1134903170, 12586269025, ...
13, 377, 10946, 2178309, 365435296162, 10610209857723, ...
89, 4181, 75025, 32951280099, 6557470319842, 2111485077978050, ...
233, 17711, 3524578, 139583862445, 72723460248141, 7540113804746346429, ...
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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:= bigomega(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..10);
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MATHEMATICA
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A[n_, k_] := Module[{F = Fibonacci, h, p, q = 2}, p[_] = {}; While[ Length[p[k]] < n, q = q+1; h = PrimeOmega[F[q]]; p[h] = Append[p[h], F[q]]]; p[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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