|
%I #23 Feb 05 2021 11:27:51
%S 2,21,3,8,34,5,6765,610,55,13,2584,196418,987,377,89,144,701408733,
%T 317811,10946,4181,233,832040,102334155,1134903170,2178309,75025,
%U 17711,1597,86267571272,267914296,12586269025,365435296162,32951280099,3524578,121393,28657
%N 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.
%H Alois P. Heinz, <a href="/A303216/b303216.txt">Antidiagonals n = 1..16, flattened</a>
%F A(n,k) = A000045(A303215(n,k)).
%F A001222(A(n,k)) = k.
%e Square array A(n,k) begins:
%e 2, 21, 8, 6765, 2584, 144, ...
%e 3, 34, 610, 196418, 701408733, 102334155, ...
%e 5, 55, 987, 317811, 1134903170, 12586269025, ...
%e 13, 377, 10946, 2178309, 365435296162, 10610209857723, ...
%e 89, 4181, 75025, 32951280099, 6557470319842, 2111485077978050, ...
%e 233, 17711, 3524578, 139583862445, 72723460248141, 7540113804746346429, ...
%p F:= combinat[fibonacci]: with(numtheory):
%p A:= proc() local h, p, q; p, q:= proc() [] end, 2;
%p proc(n, k)
%p while nops(p(k))<n do q:= q+1;
%p h:= bigomega(F(q));
%p p(h):= [p(h)[], F(q)]
%p od; p(k)[n]
%p end
%p end():
%p seq(seq(A(n, 1+d-n), n=1..d), d=1..10);
%t 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]]];
%t Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 10}] // Flatten (* _Jean-François Alcover_, Feb 05 2021, after _Alois P. Heinz_ *)
%Y Columns k=1-2 give: A005478, A053409.
%Y Row n=1 gives A072397.
%Y Cf. A000045, A001222, A303215, A303218.
%K nonn,tabl
%O 1,1
%A _Alois P. Heinz_, Apr 19 2018
|
