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A303217
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.
19
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
OFFSET
1,1
LINKS
FORMULA
A000045(A(n,k)) = A303218(n,k).
A001221(A000045(A(n,k))) = k.
EXAMPLE
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, ...
MAPLE
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);
MATHEMATICA
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]];
Table[A[n-k+1, k], {n, 1, nmax}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jan 04 2020 *)
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Apr 19 2018
STATUS
approved