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A303218 A(n,k) is the n-th Fibonacci number with exactly k exactly prime factors; square array A(n,k), n>=1, k>=1, read by antidiagonals. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Alois P. Heinz, Antidiagonals n = 1..18,  flattened

FORMULA

A(n,k) = A000045(A303217(n,k)).

A001221(A(n,k)) = k.

EXAMPLE

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, ...

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)[], F(q)]

        od; p(k)[n]

      end

    end():

seq(seq(A(n, 1+d-n), n=1..d), d=1..12);

CROSSREFS

Column k=3 gives A137563.

Row n=1 gives: A060319.

Cf. A000045, A001221, A303216, A303217.

Sequence in context: A249646 A143247 A303216 * A162536 A100980 A122509

Adjacent sequences:  A303215 A303216 A303217 * A303219 A303220 A303221

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Apr 19 2018

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)