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A303217
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A(n,k) is the n-th index of a Fibonacci number with exactly k distinct prime factors; square array A(n,k), n>=1, k>=1, read by antidiagonals.
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19
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3, 8, 4, 15, 9, 5, 20, 16, 10, 6, 30, 24, 18, 12, 7, 40, 36, 27, 21, 14, 11, 70, 48, 42, 28, 33, 19, 13, 60, 81, 54, 44, 32, 35, 22, 17, 80, 72, 104, 56, 45, 52, 37, 25, 23, 90, 84, 110, 105, 64, 50, 55, 38, 26, 29, 140, 126, 88, 112, 136, 78, 57, 74, 39, 31, 43
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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:
3, 8, 15, 20, 30, 40, 70, 60, 80, 90, ...
4, 9, 16, 24, 36, 48, 81, 72, 84, 126, ...
5, 10, 18, 27, 42, 54, 104, 110, 88, 165, ...
6, 12, 21, 28, 44, 56, 105, 112, 96, 256, ...
7, 14, 33, 32, 45, 64, 136, 114, 100, 258, ...
11, 19, 35, 52, 50, 78, 148, 128, 108, 266, ...
13, 22, 37, 55, 57, 92, 152, 130, 132, 296, ...
17, 25, 38, 74, 63, 95, 164, 135, 138, 304, ...
23, 26, 39, 77, 66, 99, 182, 147, 156, 322, ...
29, 31, 46, 85, 68, 102, 186, 154, 184, 369, ...
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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)[], (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; maxIndex = 200;
nu[n_] := nu[n] = PrimeNu[Fibonacci[n]];
col[k_] := Select[Range[maxIndex], nu[#] == k&];
T = Array[col, nmax];
A[n_, k_] := T[[k, n]];
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CROSSREFS
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Columns k=2-16 give: A114842, A114841, A114843, A114840, A114839, A114838, A114837, A114836, A114826, A114825, A114824, A114823, A117529, A117551, A117550.
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KEYWORD
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AUTHOR
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STATUS
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approved
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